Open AccessI-Primal Submodules
Author(s) -
Steven Steven
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1245/1/012049
Subject(s) - mathematics , prime (order theory) , primality test , element (criminal law) , ideal (ethics) , prime element , commutative ring , generalization , prime ideal , combinatorics , discrete mathematics , commutative property , mathematical analysis , philosophy , epistemology , political science , law
In module over commutative ring with identity, prime notions of submodule are growing vastly. Furthermore, there are also notions of primal submodules. Suppose N be a submodule of R -module M . An element r of R is called prime to N if rm ∈ N with m element of M implies m ∈ N . The submodule N is called primal if the set of elements which not prime to N forms an ideal. The generalization of elements which prime to N is proposed and referred as elements that almost prime to N . An element r ∈ R is called almost prime to N if rm ∈ N – ( N : M ) N for m element of M implies m is an element of N . In this article, we introduce the generalization of elements which are prime to N as elements which are I -prime to N by changing the set ( N : M ) into an arbitrary ideal of R. With this notion, we can generalize primality of submodule N to I -primality of submodule N . We called N the submodule of M is I -primal submodule if the set of elements which are I -prime to N forms an ideal of R . Furthermore, we give some characterizations of I -primal submodules and their relation to other prime and primal notions.