A Prime Ideal Principle in commutative algebra

On Commutative Algebra Homology in Prime Characteristics

We give decompositions of the Hochschild and cyclic homology of a com-mutative algebra in characteristic p into p?1 parts, and show these decom-positions are compatible with the shuue product structures. We also give a counterexample to a conjecture attributed to Barr, which asserts that a modiied version of Harrison cohomology coincides with Andr e/Quillen cohomology.

T-Rough (Prime, Primary) Ideal and T-Rough Fuzzy (Prime, Primary) Ideal on Commutative Rings

The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...

Maximal ideal space of a commutative coefficient algebra

The basic notion of the article is a pair (A, U), whereA is a commutative C-algebra and U is a partial isometry such thatA ∋ a → UaU is an endomorphism of A and UU ∈ A. We give a description of the maximal ideal space of the smallest coefficient C-algebra E∗(A) of the algebra C(A, U) generated by the system (A, U).

A (one-sided) Prime Ideal Principle for Noncommutative Rings

In this paper we study certain families of right ideals in noncommutative rings, called right Oka families, generalizing previous work on commutative rings by T.Y. Lam and the author. As in the commutative case, we prove that the right Oka families in a ring R correspond bijectively to the classes of cyclic right R-modules that are closed under extensions. We define completely prime right ideal...

Commutative Algebra Commutative Algebra : General