Our purpose in this paper is to characterize skew PBW extensions over several weak symmetric rings. As a consequence of our treatment, we extend results the literature concerning property symmetry for commutative rings and polynomial

In view of this theorem, the study of the structure of commutative algebras with unity element satisfying an identity of degree g 4 is immediately reduced to the study of algebras satisfying one of the identities (l)-(3). The first of these identities is well-known to be equivalent to power-associativity in a commutative algebra of characteristic not 2, 3, or 5 and has been studied extensively ...

Combinatorial commutative algebra is a branch of combinatorics, discrete geometry, and commutative algebra. On the one hand, problems from combinatorics or discrete geometry are studied using techniques from commutative algebra; on the other hand, questions in combinatorics motivated various results in commutative algebra. Since the fundamental papers of Stanley (see [13] for the results) and H...

We study actions of pointed Hopf algebras in the Z-graded setting. Our main result classifies inner-faithful generalized Taft on quantum Weyl which respect Z-grading. also show that generically invariant rings are commutative rings.

Introduction Commutativity theorems are part of the study of polynomial identities in noncommutative rings. They are theorems which assert that, under certain conditions, the ring at hand must be commutative. The proofs of theorems of this sort in their general form require the structure theory for non-commutative rings. Instances of these theorems have a strongly computational flavor. They pro...

We introduce the notion of a Hu-Liu prime ideal in the context of left commutative rngs, and establish the contravariant functor from the category of left commutative rngs into the category of topological spaces. It is well known that new points must be introduced in order to expand algebraic geometry over algebraically closed fields into Grothendieck’s scheme theory over commutative rings. We ...

We prove that pure morphisms of commutative rings are effective Adescent morphisms where A is a (COMMUTATIVE RINGS)-indexed category given by (i) finitely generated modules, or (ii) flat modules, or (iii) finitely generated flat modules, or (iv) finitely generated projective modules.

A commutative ring A is said to be clean if every element of A can be written as a sum of a unit and an idempotent. This definition dates back to 1977 where it was introduced by W. K. Nicholson [7]. In 2002, V. P. Camillo and D. D. Anderson [1] investigated commutative clean rings and obtained several important results. In [4] Han and Nicholson show that if A is a semiperfect ring, then A[Z2] i...

Let A be a commutative augmented ring and I its augmentation ideal. This paper shows that the sequence {In/In+1} becomes stationary up to isomorphism. The result yields stability in associated graded of along I.