A Characterization Of Primal Noetherian Rings.
A generalization of the prime radical of an ideal.
A graph associated to proper non-small ideals of a commutative ring
In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring , denoted by , is a graph with all non-small proper ideals of as vertices and two distinct vertices and are adjacent if and only if is not small in . In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter,...
A note on finitely generated ideal-simple commutative semirings
Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.
A note on prime modules.
A Note on Skew Polynomial Rings
A short proof of Krull's intersection theorem
A theoreme on derivations in semiprime rings.
An algorithm for the decomposition of ideals of the group ring of a symmetric group.
An approximation theorem for Dubrovin valuation rings.
An ideal-based zero-divisor graph of direct products of commutative rings
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.
Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra
Let be the two-parameter quantized enveloping algebra and the locally finite subalgebra of under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of in the case when is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of by generators.
Associated prime ideals of skew polynomial rings.