Let $ R $ be a commutative ring and let $ M $ be an $ R $-module. In this article, we
introduce the concept of the Zariski socles of submodules of $ M $ and investigate their …

Let R be a commutative ring and let M be an R-module. Let X= Spec (M) be the prime
spectrum of M with Zariski topology. Our main purpose in this paper is to specify the …

PRIMARY-LIKE SUBMODULES AND A SCHEME OVER THE PRIMARY-LIKE SPECTRUM OF
MODULES Page 1 Miskolc Mathematical Notes HU e-ISSN 1787-2413 Vol. 18 (2017), No. 2 …

PRIMARY-LIKE SUBMODULES AND A SCHEME OVER THE PRIMARY-LIKE SPECTRUM OF
MODULES Page 1 Miskolc Mathematical Notes HU e-ISSN 1787-2413 Vol. 18 (2017), No. 2 …

Let R be a commutative ring with identity and M be a unital R-module. The primary-like
spectrum SpecL (M) is the collection of all primary-like submodules Q of M such that M/Q is a …

Let R be a commutative ring and M an R-module. The purpose of this article is to introduce a
new class of modules over R called X-injective R-modules, where X is the prime spectrum of …

Let R be a commutative ring and let M be a top R-module. In this article, we investigate some
properties of a new class of modules, called strongly top modules. Studying of this family …

Let R be a commutative ring and M be an R-module. The second spectrum Spec s (M) of M
is the collection of all second submodules of M. We topologize Spec s (M) with Zariski …

Let R be a commutative ring having nonzero identity and M be a unital R-module. Assume
that S⊆ R is a multiplicatively closed subset of R. Then, M satisfies S-Noetherian spectrum …

Inspired by the interplay between the Zariski topology defined on the prime spectrum of a
commutative ring R and the ring theoretic properties of R in [3, 8, 18, 23, 25], we introduce in …