Abstract Algebra Answers

Prove that SL(n,F) is a normal subgroup of GL(n,F)?

If R is a commutative noetherian ring and P is a prime ideal of R, then prove that an R-module is P-primary if and only if each nonzero submodule of M is subisomorphic to R/P.

Each content area in Mathematics contributes towards the acquisition of specific skills. One focus area emphasised is that “the learner should recognize and describe properties of numbers and operations, including (i) identity properties, (ii) factors, (iii) multiples, and (iv) commutative; (vi) associative and (vii) distributive properties” Describe in brief, what the identity property entails and provide two relevant examples. (Hint: use different basic operations to clarify your answer) 

let R be comutetive ring with unity in which each ideal prime then show that R is a field.

 Showthatthe Polynomial x7-1oxs+15x+5 is not Solvable by ..

f is mapping from M to N . f is an R homomorphism and M is finitely generated then prove that N is also finitely generated.

Prove that Homz(Z,M) is isomorphic to M where M is an abelian group.

Prove that if N is a submodule of a finitely generated module M over a ring R .Then M/N is also finitely generated R module.