The AlgeBabble Page

Do you wish you had sample questions to study for the Algebraic Structures final exam? Or do you just want to practice your algebra proofs? Do you want to feel completely confused? Then this is for you!

Yes, there is now an on-line stochastic algebraic structures exam question generator... the executable is ~is25/bin/structures/algebabble

(disclaimer: not responsible for loss of grades or sanity)

And just to convince you that this is the best darn proof generator around, here's some samples:

2. (53%) Let the ring-isomorphism R be given.

(a) Prove a unique kernel of R is the kernel such that a unique homomorphism of R is a subset of the isomorphism.
(b) Show that a unique homomorphism on R is a field of fractions such that a unique homomorphism of R is a proper subset of a unique isomorphism (cf. Text, p. 102).
HINT: Recall a subring with a unique isomorphism of R is a kernel of a field of fractions.

2. (48%) Let the monoid M be given, and let the group G in G' be given.

(a) Prove that a field of G is the field of fractions (cf. Text, p. 273).
(b) Prove a unique division ring of G is a submonoid such that a field of R is isomorphic to a field.
HINT: Consider the division ring with the division ring of M is a kernel of a unity.
(c) Show the neuter is a subring.
(d) Prove that the division ring is the only unity (cf. Text, p. 61).

3. (62%) Let the group-isomorphism G be given, and let us define the group-isomorphism G' on G .

(a) Show that the subring is a field of fractions.
(b) Deduce that the only kernel on G is a unique division ring (cf. Text, p. 156).

But don't just take our word for it, here's some satisfied customers:

"Before, I never knew how to study for Structures. Now, I can bang my head against the wall while doing impossible proofs. Thanks, algebabble!"

--Moe Noid

"After a month of research, I finally solved an algebabble proof. The professor was so impressed, he gave me an A and I didn't even have to take the course!"

--Bo Ring

"Algebabble even gave me random pages in the text to look for clues that aren't there! And the best part is, I can't tell the difference between algebabble questions and the real test questions."

--Dee Deuce

"This is the best thing to come along since saturday morning cartoons!"

--The IsoMorphin' Power Rangers

(Yes, this program really exists)

Received 05-11-1995 from Ian Schreiber

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