Let A⊆ B be a commutative ring extension such that B is a trivial extension of A (denoted by
A∝ E) or an amalgamated duplication of A along some ideal of A (denoted by A⊳⊲ I). This …

Let A⊆ B be a commutative ring extension such that B is a trivial extension of A (denoted by
A∝ E) or an amalgamated duplication of A along some ideal of A (denoted by A⋈ I). This …

In this paper we investigate the conditions under which a given ring is a sub-ring of a semi-
simple ring. 1 For convenience, we say that a ring A is an extension of a ring B, if B is a sub …

Let△ be a multiplicatively closed set of finitely generated nonzero ideals of a ring R. Then
the concept of a△-reduction of an R-submodule D of an R-module A is introduced and …

We study properties of cancellation ideals of ring extensions. Let R Ç S be a ring extension.
A nonzero S-regular ideal I of R is called a (quasi)-cancellation ideal of the ring extension R …

A module M is said to be FI-extending if every fully invariant submodule of M is essential in a
direct summand of M. A ring R is right FI-extending if every ideal of R is right essential in an …

Let $ R=(B, E) $ be the split-null or trivial extension of a faithful module $ E $ over a
commutative ring $ B $. $ R $ is an FPF ring iff the partial quotient ring $ B {S^{-1}} $ with …

Let f WA! B be a ring homomorphism and J an ideal of B. In this paper, we initiate a
systematic study of a new ring construction called the “amalgamation of A with B along J with …

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. In
this article we introduce a new class of ring, called S-multiplication rings which are S …

All rings are commutative with identity and all modules are unital. Let R be a ring and M an R-
module. In our recent work we investigated faithful multiplication modules and the properties …