BHASKAR

i think every simple ring is artinian, trivially as no ideals in simple ring implies DCC trivially.

but then i am stuck in wedderburn artin theory. please help

i have found several solutions over the net, the one i want to understand uses Hilbert's irreducibility theorem whose proof i understood more or less , but my problem is with the solution now.

this proof is going as to prove that f (x, y) = y^n - xy - x in Q[x, y] has Galois group

G = Sn over Q(x), and then we can use Hilbert's irreducibility theorem.

1st step : for any r ∈ Q, the Galois group of f (r, y) ∈ Q[ y] over Q injects canonically in

the Galois group of f (x, y) over Q(x). what is the mapping?

2) f(y) is irreducible over Q(x) by Eisenstein’s criterion?? how?? eisenstein criterion determines irreducibility of polynomials over UFD where there is a prime element s.t blah blah...

f(y)∈ Q[x][y] so what is the prime element in Q[x] which satisfies eisenstein criterion for f(y)??

first please help me understand these two things... rest is one more important step which i will post later after understanding this. please help...

Just don't kill me or kiss me, soon enough,

unless you are afraid, of a coward like me,

you got the wand of life, can swing anytime,

but play a fair game, i won't cheat you, you don't cheat me.

I won't beat you, you don't cheat me,

an arrow at your headlevel, just won't kill you,

you've created me, the whole ******* world,

but my quest is your secret, how will you end all this?

A space free of topology, a space which could bend,

which you hiding in your pocket, ain't there no more,

don't look around, stolen by the best con man ever,

sold to Mr.reality, whom you killed thousand years ago.

It's just, all my friends are here, but you are not,

as omnipresent you are, still lost in realistic fog,

you try on your end, and i try on mine end,

may be you control the fog, but i will master in space and time.

No battle you offer, none i accept your baits,

a man to man challenge, shall we see in time, in future,

but it's the best fight ever, neither i can reach you, none you can fall down,

shall we compromise, before my drink go down and i raise my parker pen.

If i could walk two more steps,

If i could look down that hill,

I'd be frozen in time, swallowed in peace,

If i could look away when you smiled.

Like an unspoken word, just stuck on lips,

like a water drop, frozen on the edge of a cloud ,

I was triggered, and i was fired towards the moon,

when from nowhere, stupid sun replaced the moon.

Going with the wind, but the wind took me back,

tried to be a bird,but got eaten by worms,

I swear i was alive, just don't remember when last time,

If i could write a song, i'd begin from the end.

If somebody listen to what i say,

there will be words unheard and melodies unsung,

I could colour up this world gray and white,

If i could walk two more steps, one to the left, one to the right.

It could have been a boulevard and hopes chirping around,

what now is a dead calm sea full of tears, and a black sun,

that shooting star could have fulfilled every wish,

If i could look down that hill, when i was about to jump.

Nothing would be here, but a dead heart flying,

beating or not, but glittering through the sky,

could have lit up this dark, just like that shooting star,

If i could look away when you smiled, at that shooting star.

like a glass of whisky frozen in ice, wonder when i ll melt,

thrown away, before melting, by the one who was going to drink it,

like an umbrella opened under clouds,

but it didn't rain when it was supposed to.

fog it is inside me, but still i can see what you think,

once was there around you, now not even in your thoughts.

think of me someday, and talk to me in your dreams.

and may be, for a moment we'll be together in imagination divine.

take me anywhere, as long as i am in your thoughts,

wake up from sleep, and i ll be lost from your dreams,

will fall into lullaby of death, and the story will change,

where i was supposed to die, but the lullaby ll make me alive.

contradicting my death, dogs will be chasing my life,

but you can can throw them a bone, a bone full of life,

who else is there who can save me from these dogs without teeth,

tore me apart, but still you can join me and i can thrive.

i would have swore, if you weren't so alive,

like an icon who can see, but so shy to feel,

just think of me as a demon, looking for a bride,

stealing you from you, could be my eternal crime.

i need conceptual history, not dates and names, what brought the concept and how these two subjects combine i.e. why we study them together, what led to it.

Come, hold my hand and step into my dreams,

walk around in my mind wrapped in my thoughts,

don't look for stars or sunshine down that road,

come find me in those dark, dark black holes.

I will send my conciousness back on vacation,

Will lie sleeping for many many days,

You go around and enjoy the view,

this whole paradise was build for you.

Just a little request, don't scratch on the walls,

You will leave in few hours, but those will hurt for a while,

and don't turn left on 66th street,

There are rumors about a ghost who is obessesed about you.

I wish i could give you a map for dreamtown,

But it wasn't me who built most of the town,

there used to be a waterfall few days ago,

either it disappeared or froze up under fake snow.

I put a sun to keep you warm, rain for delight,

Night will be cold, just for the feeling you looking for,

I don't know for sure will you ever arrive,

but if you will, and won't find me,

Take a tour and while stepping out, just look back once before you go out.

Come, hold my hand and step into my dreams,

walk around in my mind wrapped in my thoughts,

don't look for stars or sunshine down that road,

come find me in those dark, dark black holes.

I will send my consciousness back on strike,

will sleep long enough, may not even look alive,

and then you walk around and enjoy the view,

this whole paradise was build for you.

Just a little request, don't scratch on the walls,

you will leave in few hours, but those will hurt for a while,

and do not turn left on 66th street,

there were rumors about a ghost who was obsessed about you.

I wish i could give you a map for dreamtown,

but it wasn't me who built most of the town,

there used to be a waterfall few days ago,

either reality drank it or froze up under fake snow.

I put a sun to keep you warm and rain for delight,

night will be cold, so you look red like a rose,

i am not sure sure if you will ever come,

but if you will, and won't find me,

take a tour around and look back once before stepping out.

I am a maths student in masters, i want to study philosophy from beginners level, for leisure activity, not interested in any political, economical or one kind of philosophy of some one man like marxist and all. i want to study from the beginners level, about philosophy, as abstract as possible, i like to think, so i want to spend some time with philosophy books, later on going to metaphysics and theology. i want to study on my own, so looking for books, step by step which can raise my intereset in the subject. please recoomend me books for each level, and books which are really good to self study.

i will be very thankful to you.

xperia ZL is around 4-5k cheaper then Z.

but on specifications both look almost same. i am thinking of buying ZL but it Z has some hidden extra features please tell me so i can reconsider.

i dont understand why ZL has less price and less advertisements.

has it any serious faults which sony does not want to advert.

plz tell

i want to ask that what a homomorphism of two groups or rings mean.

like isomorphism says both enjoys same structural property that if we study one such object we know about all isomorphic objects.

what can we say about homomorphic images.

or any other suggestion in these two ranges, better then these.

is there any internet site or dictionary which tell me urdu words for english or hindi words but doesnt display it in urdu fonts but in hindi fonts.

like if i write worship to it gives me ibaadat but not ibaadat in urdu language. because i cant read urdu.

i went to a book fair and i found a

book on number theory, it looked

very conceptual and different from

other texts. its index was very friendly

stuff. i forgot the name of author or

exact name of book.

but it was hardcover and had a

monkey/chimpanzee face on front

cover. can anyone tell me which was

it?

it costed around 8000 INR.

i went to a book fair and i found a book on number theory, it looked very conceptual and different from other texts. its index was very friendly stuff. i forgot the name of author or exact name of book.

but it was hardcover and had a monkey/chimpanzee face on front cover. can anyone tell me which was it?

it costed around 8000 INR.

If the sun stopped shining, there might be some reason,

Clouds, eclipse, or could be a beast swallowed Mr.SUN,

If the river dried up in such heavy monsoon,

Lava, thirsty shadow, or could be a wormhole beneath my toe.

Tomorrow headed back, yesterday still to come,

It doesnt happen everyday,

could be you, could be me,

or just another tuesday,

Clocks are flying, and pigeons telling time,

There could be a reason disguised in this rhyme.

If eyes crying blood, hearts bleeding water,

There must be something wrong, still doctor does not care,

Whose fault is this which brought this chaos?

Stop asking this, and look for the cause of chaos.

It wasnt long ago, when sun used to glitter,

It feels like tomorrow, when i used to swim in that river,

On previous today, tomorrow wasn't confused,

Clocks weren't drunk and pigeons used to fly.

Either bring back those days, or its hard to survive ,

Its not that hard if i try, I might just rethrive,

put my head in my stomach and heart on the shelf,

may be no one will regret except a few dreams, dead destiny, and those moments been shot.

Its like a river is flowing out of me,

a river of tears,

Today i m down in the ground,

six feet under.

I need a cup of life, flavoured with smile,

cup without bottom,

Need to slide down from the cliff of despair,

to climb one more time.

I am thirsty and still riding towards a desert,

desert without U turn,

There is a mirror following me into this abyss,

abyss full of mirrors.

There is no way out of the dimension i am in,

a dimension, dimensionless,

Lost in, half full of void, half nill of fill ,

smoking on an underground hill.

Give me a pill of dreams wrapped around a gun,

a pill to swallow,

I wish for a wish that i could wish,

a wish lost long ago.

Sometimes when i look out, i wish it start to rain,

rain drops black and dry,

Why do i even try?,

try to breath, try to survive.

Its like a river is flowing out of me,

a river of tears,

Today i m down in the ground,

six feet under.

I need a cup of life, flavoured with smile,

cup without bottom,

Need to slide down from the cliff of despair,

to climb one more time.

I am thirsty and still riding towards a desert,

desert without U turn,

There is a mirror following me into this abyss,

abyss full of mirrors.

There is no way out of the dimension i am in,

a dimension, dimensionless,

Lost in, half full of void, half nill of fill ,

smoking on an underground hill.

Give me a pill of dreams wrapped around a gun,

a pill to swallow,

I wish for a wish that i could wish,

a wish lost long ago.

Sometimes when i look out, i wish it start to rain,

rain drops black and dry,

Why do i even try?,

try to breath, try to survive.

Its like a river is flowing out of me,

a river of tears,

Today i m down in the ground,

six feet under.

I need a cup of life, flavoured with smile,

cup without bottom,

Need to slide down from the cliff of despair,

to climb one more time.

I am thirsty and still riding towards a desert,

desert without U turn,

There is a mirror following me into this abyss,

abyss full of mirrors.

There is no way out of the dimension i am in,

a dimension, dimensionless,

Lost in, half full of void, half nill of fill ,

smoking on an underground hill.

Give me a pill of dreams wrapped around a gun,

a pill to swallow,

I wish for a wish that i could wish,

a wish lost long ago.

Sometimes when i look out, i wish it start to rain,

rain drops black and dry,

Why do i even try?,

try to breath, try to survive.

Opened my door tonight, felt the one i was waiting for,

which called for my soul to return from the sunny shore,

i couldn't ask for more, while it was just a few steps away,

just kiss me on my lips, and stay for always.

Darkness in the nights will now wear white jewels,

they look so pretty when they are cold and cruel,

my lonliness stopped crying and is smiling again,

wait is almost over ,dear, winter is finally coming.

Take me on a ride, where i can be dead in snow,

fog give my eulogy and quiet carry my corpse,

give me my freedom, from the prison of summer,

sun is a felon, in the realm of this king.

Talking to silence in the winter nights,

beading my thoughts with pearls of ice,

chillness in my soul will wash away the fire,

the fire bothering me since i am alive.

We can go in calm , and shake our souls,

spill away all the chaos and refill it with void,

what a lotion winter brings which heals the dead souls,

along with her dark sword to cut through fake glows.

To welcome her you don't need flowers or fire,

just dark the lightness and sing in silence,

push yourself from the heights you have achieved,

get buried in the mist of truth and find the reality.

Just put your head in her lap, and she will sing you a lullaby,

you can kill those lizards in your in mind and she will be your alibi,

fill me with emptiness, and make me your heir,

may she gallop me in this time, and make me a part of her.