Abstract
Let be a commutative ring with an identity and be a unitary -module. We say that a non-zero submodule of is primary if for each with en either or and an -module is a small primary if = for each proper submodule small in. We provided and demonstrated some of the characterizations and features of these types of submodules (modules).
Highlights
A non-zero submodule of is called primary if whenever and with implies that √or
As for this research, we present and study a generalization of the concepts of small primary submodule and small primary module as follows; We call a submodule of as a small primary submodule if whenever is small in and
This research consists of two parts; in the first part, we present the definition of small primary submodules and discuss some of their relationships with some types of the previously studied submodules and gave the conditions of equivalence between them
Summary
For each proper submodule of [1]. These two concepts were generalized by many researchers [2, 3, 4]. As for this research, we present and study a generalization of the concepts of small primary submodule and small primary module as follows; We call a submodule of as a small primary submodule if whenever is small in and. This research consists of two parts; in the first part, we present the definition of small primary submodules and discuss some of their relationships with some types of the previously studied submodules and gave the conditions of equivalence between them. We present a definition of small primary modules and study and demonstrate some of their properties in detail. 2- Small Primary Submodules Definition (2.1): i) A non-zero submodule of -module is called small primary iff whenever.
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