On matrices with elements in a principal ideal ring

Rings with Every Proper Image a Principal Ideal Ring

The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension such that every proper homomorphic image is a...

Similarity Classes of 3× 3 Matrices over a Local Principal Ideal Ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.

Concerning Matrices with Elements in a Commutative Ring*

On Ideal Elements in Poe-AG-groupoid

In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...

Notes on amalgamated duplication of a ring along an ideal

In this paper, we study some ring theoretic properties of the amalgamated duplication ring $Rbowtie I$ of a commutative Noetherian ring $R$ along an ideal $I$ of $R$ which was introduced by D'Anna and Fontana. Indeed, it is determined that when $Rbowtie I$ satisfies Serre's conditions $(R_n)$ and $(S_n)$, and when is a normal ring, a generalized Cohen-Macaulay ring and finally a filter ring.