In this paper, we study the notion of divided and regular divided rings. Then we establish the
transfer of these notions to trivial ring extension and amalgamated algebras along an ideal …

In this paper, we introduce a generalization of the well-known notion of a “weak hereditary”
ring and a “P-hereditary” ring, which we call a “weak P-hereditary” ring. We investigate the …

In this paper, we introduce and study the notion of “v-Noetherian rings" which is a notion
between Noetherian rings and v-coherent rings. Then we establish the transfer of this notion …

Let R be a commutative ring with identity and let I be an ideal of R. Let the subring of R× R
consisting of the elements (r, r+ i) for r∈ R and i∈ I. Introduce a new general construction …

Let R be a commutative ring with identity and let I be an ideal of R. In this paper we study the
amalgamated duplication ring R⋈ I introduced by D'Anna and Fontana. By assuming that (1 …

Let S be a commutative semigroup with 0. The zero-divisor graph Γ (S) of S is the graph
whose vertices are nonzero zero-divisors of S, and two vertices x and y are adjacent if xy= 0 …

In this paper, we consider five possible extensions of the Pr\" ufer domain notion to the case
of commutative rings with zero-divisors. We investigate the transfer of these Pr\" ufer-like …

Clean Property in Subring Retracts 1 Introduction Page 1 International Mathematical Forum, 4,
2009, no. 21, 1039 - 1043 Clean Property in Subring Retracts Chahrazade Bakkari …

Let R be a commutative ring and M be an R-module. The idealization R (+) M (also called
the trivial extension), introduced by Nagata in 1956, is a ring where the module M can be …