ON ALMOST PRIME SUBMODULES OF A MODULE OVER A PRINCIPAL IDEAL DOMAIN

2016 ◽  
Vol 38 (2) ◽  
pp. 121-128
Author(s):  
I Gede Adhitya Wisnu Wardhana ◽  
Pudji Astuti ◽  
Intan Muchtadi-Alamsyah
Keyword(s):  
Principal Ideal ◽  
Principal Ideal Domain ◽  
Ideal Domain ◽  
Prime Submodules ◽  
Almost Prime

scholarly journals A note on almost prime submodule of CSM module over principal ideal domain

2021 ◽  
Vol 2106 (1) ◽  
pp. 012011
Author(s):  
I G A W Wardhana ◽  
N D H Nghiem ◽  
N W Switrayni ◽  
Q Aini
Keyword(s):  
Prime Ideal ◽  
Algebraic Structure ◽  
Principal Ideal ◽  
Ring Theory ◽  
Principal Ideal Domain ◽  
Module Theory ◽  
Ideal Domain ◽  
Multiplication Operation ◽  
Prime Submodule ◽  
Almost Prime

Abstract An almost prime submodule is a generalization of prime submodule introduced in 2011 by Khashan. This algebraic structure was brought from an algebraic structure in ring theory, prime ideal, and almost prime ideal. This paper aims to construct similar properties of prime ideal and almost prime ideal from ring theory to module theory. The problem that we want to eliminate is the multiplication operation, which is missing in module theory. We use the definition of module annihilator to bridge the gap. This article gives some properties of the prime submodule and almost prime submodule of CMS module over a principal ideal domain. A CSM module is a module that every cyclic submodule. One of the results is that the idempotent submodule is an almost prime submodule.

scholarly journals Notes on topological rings

2013 ◽  
Vol 29 (2) ◽  
pp. 267-273
Author(s):  
MIHAIL URSUL ◽  
◽  
MARTIN JURAS ◽  
Keyword(s):  
Principal Ideal ◽  
Principal Ideal Domain ◽  
Compact Ring ◽  
Ring Topology ◽  
Bezout Domain ◽  
Totally Bounded ◽  
Ideal Domain ◽  
Nilpotent Ring ◽  
Trivial Multiplication

We prove that every infinite nilpotent ring R admits a ring topology T for which (R, T ) has an open totally bounded countable subring with trivial multiplication. A new example of a compact ring R for which R2 is not closed, is given. We prove that every compact Bezout domain is a principal ideal domain.

Invariant Factors Under Rank One Perturbations

1980 ◽  
Vol 32 (1) ◽  
pp. 240-245 ◽  
Author(s):  
Robert C. Thompson
Keyword(s):  
Commutative Ring ◽  
Principal Ideal ◽  
Matrix Multiplication ◽  
Diagonal Form ◽  
Principal Ideal Domain ◽  
Ideal Domain ◽  
Zero Divisors ◽  
Rank One ◽  
Invariant Factors

Let R be a principal ideal domain, i.e., a commutative ring without zero divisors in which every ideal is principal. The invariant factors of a matrix A with entries in R are the diagonal elements when A is converted to a diagonal form D = UAV, where U, V have entries in R and are unimodular (invertible over R), and the diagonal entries d1 …, dn of D form a divisibility chain: d1|d2| … |dn. Very little has been proved about how invariant factors may change when matrices are added. This is in contrast to the corresponding question for matrix multiplication, where much information is now available [6].

scholarly journals Finitely generated cyclic extensions of free groups are residually finite

1971 ◽  
Vol 5 (1) ◽  
pp. 87-94 ◽  
Author(s):  
Gilbert Baumslag
Keyword(s):  
Free Group ◽  
Principal Ideal ◽  
Free Groups ◽  
Cyclic Extension ◽  
Principal Ideal Domain ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Residually Finite ◽  
Ideal Domain ◽  
Direct Sum

We establish the result that a finitely generated cyclic extension of a free group is residually finite. This is done, in part, by making use of the fact that a finitely generated module over a principal ideal domain is a direct sum of cyclic modules.

scholarly journals Decomposition of representation algebras

1969 ◽  
Vol 10 (3-4) ◽  
pp. 395-402 ◽  
Author(s):  
W. D. Wallis
Keyword(s):  
Finite Group ◽  
Principal Ideal ◽  
Isomorphism Class ◽  
Principal Ideal Domain ◽  
Ideal Domain ◽  
A Finite Group

Throughout this paper g is a finite group and f is a complete local principal ideal domain of characteristic p where p divides |g|. The notations of [5] are adopted; moreover we shall denote the isomorphism-class of an f g-representation module ℳ by M, the class of ℳx by Mx and the class of ℳR by MR for suitable groups K and R.

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