On the ring of endomorphisms of a multiplication module

1994 ◽  
Vol 29 (3) ◽  
pp. 277-284 ◽  
Author(s):  
A. G. Naoum
Keyword(s):  
Multiplication Module ◽  
Ring Of Endomorphisms

scholarly journals On a generalization of prime submodules of a module over a commutative ring

2017 ◽  
Vol 37 (1) ◽  
pp. 153-168
Author(s):  
Hosein Fazaeli Moghimi ◽  
Batool Zarei Jalal Abadi
Keyword(s):  
Commutative Ring ◽  
Dedekind Domain ◽  
Finitely Generated ◽  
Multiplication Module ◽  
Maximal Ideals ◽  
Prime Submodules ◽  
Prime Submodule

‎Let $R$ be a commutative ring with identity‎, ‎and $n\geq 1$ an integer‎. ‎A proper submodule $N$ of an $R$-module $M$ is called‎ ‎an $n$-prime submodule if whenever $a_1 \cdots a_{n+1}m\in N$ for some non-units $a_1‎, ‎\ldots‎ , ‎a_{n+1}\in R$ and $m\in M$‎, ‎then $m\in N$ or there are $n$ of the $a_i$'s whose product is in $(N:M)$‎. ‎In this paper‎, ‎we study $n$-prime submodules as a generalization of prime submodules‎. ‎Among other results‎, ‎it is shown that if $M$ is a finitely generated faithful multiplication module over a Dedekind domain $R$‎, ‎then every $n$-prime submodule of $M$ has the form $m_1\cdots m_t M$ for some maximal ideals $m_1,\ldots,m_t$ of $R$ with $1\leq t\leq n$‎.

Strongly 0-dimensional Modules

2014 ◽  
Vol 57 (1) ◽  
pp. 159-165 ◽  
Author(s):  
Kürşat Hakan Oral ◽  
Neslihan Ayşen Özkirişci ◽  
Ünsal Tekir
Keyword(s):  
Multiplication Module ◽  
Finite Intersection ◽  
Von Neumann ◽  
Prime Submodules ◽  
Von Neumann Regular ◽  
Prime Submodule ◽  
Dimensional Module

AbstractIn a multiplication module, prime submodules have the following property: if a prime submodule contains a finite intersection of submodules, then one of the submodules is contained in the prime submodule. In this paper, we generalize this property to infinite intersection of submodules and call such prime submodules strongly prime submodules. A multiplication module in which every prime submodule is strongly prime will be called a strongly 0-dimensional module. It is also an extension of strongly 0-dimensional rings. After this we investigate properties of strongly 0-dimensional modules and give relations of von Neumann regular modules, Q-modules and strongly 0-dimensional modules

Permutation endomorphisms and refinement of a theorem of Birkhoff

1960 ◽  
Vol 56 (4) ◽  
pp. 322-328 ◽  
Author(s):  
H. K. Farahat ◽  
L. Mirsky
Keyword(s):  
Abelian Group ◽  
Finite Number ◽  
Linear Combination ◽  
Finite Linear Combination ◽  
Usual Manner ◽  
Restricted Permutation ◽  
Image Position ◽  
Ring Of Endomorphisms ◽  
Finite Linear

Let be a free additive abelian group, and let be a basis of , so that every element of can be expressed in a unique way as a (finite) linear combination with integral coefficients of elements of . We shall be concerned with the ring of endomorphisms of , the sum and product of the endomorphisms φ, χ being defined, in the usual manner, by the equationsA permutation of a set will be called restricted if it moves only a finite number of elements. We call an endomorphism of a permutation endomorphism if it induces a restricted permutation of the basis .

Arithmetic modules over generalized Dedekind domains

2020 ◽  
pp. 2250045
Author(s):  
Indah Emilia Wijayanti ◽  
Hidetoshi Marubayashi ◽  
Iwan Ernanto ◽  
Sutopo
Keyword(s):  
Free Module ◽  
Dedekind Domain ◽  
Finitely Generated ◽  
Multiplication Module ◽  
Dedekind Domains ◽  
Torsion Free Module ◽  
Polynomial Module ◽  
Torsion Free

Let [Formula: see text] be a finitely generated torsion-free module over a generalized Dedekind domain [Formula: see text]. It is shown that if [Formula: see text] is a projective [Formula: see text]-module, then it is a generalized Dedekind module and [Formula: see text]-multiplication module. In case [Formula: see text] is Noetherian it is shown that [Formula: see text] is either a generalized Dedekind module or a Krull module. Furthermore, the polynomial module [Formula: see text] is a generalized Dedekind [Formula: see text]-module (a Krull [Formula: see text]-module) if [Formula: see text] is a generalized Dedekind module (a Krull module), respectively.

On the compressed essential graph of a module over a commutative ring

2020 ◽  
pp. 2150125
Author(s):  
S. H. Payrovi ◽  
S. Babaei ◽  
E. Sengelen Sevim
Keyword(s):  
Commutative Ring ◽  
Undirected Graph ◽  
Finitely Generated ◽  
Multiplication Module ◽  
Essential Ideal

Let [Formula: see text] be a commutative ring and [Formula: see text] be an [Formula: see text]-module. The compressed essential graph of [Formula: see text], denoted by [Formula: see text] is a simple undirected graph associated to [Formula: see text] whose vertices are classes of torsion elements of [Formula: see text] and two distinct classes [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] is an essential ideal of [Formula: see text]. In this paper, we study diameter and girth of [Formula: see text] and we characterize all modules for which the compressed essential graph is connected. Moreover, it is proved that [Formula: see text], whenever [Formula: see text] is Noetherian and [Formula: see text] is a finitely generated multiplication module with [Formula: see text].

scholarly journals Multiplication Modules

1979 ◽  
Vol 22 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Surjeet Singh ◽  
Fazal Mehdi
Keyword(s):  
Multiplication Module

All rings R considered here are commutative with identity and all the modules are unital right modules. As defined by Mehdi [6] a module MR is said to be a multiplication module if for every pair of submodules K and N of M, K ⊂ N implies K=NA for some ideal A of R. This concept generalizes the well known concept of a multiplication ring.

Summability of a ring of endomorphisms of vector groups

1998 ◽  
Vol 37 (1) ◽  
pp. 48-55
Author(s):  
A. M. Sebel’din
Keyword(s):  
Ring Of Endomorphisms

scholarly journals Choice of Confounding in the 2k Factorial Design in 2b Blocks

2019 ◽  
pp. 50-56
Author(s):  
Francis C. Eze
Keyword(s):  
Factorial Design ◽  
Linear Combination ◽  
Incomplete Block ◽  
Multiplication Module ◽  
Principal Block ◽  
Randomized Design ◽  
Number Of Factors ◽  
Completely Randomized Design ◽  
Homogeneous Block ◽  
Number Of Treatment

In 2k complete factorial experiment, the experiment must be carried out in a completely randomized design. When the numbers of factors increase, the number of treatment combinations increase and it is not possible to accommodate all these treatment combinations in one homogeneous block. In this case, confounding in more than one incomplete block becomes necessary. In this paper, we considered the choice of confounding when k > 2. Our findings show that the choice of confounding depends on the number of factors, the number of blocks and their sizes. When two more interactions are to be confounded, their product module 2 should be considered and thereafter, a linear combination equation should be used in allocating the treatment effects in the principal block. Other contents in other blocks are generated by multiplication module 2 of the effects not in the principal block. Partial confounding is recommended for the interactions that cannot be confounded.

On 2-Absorbing Submodules

2012 ◽  
Vol 19 (spec01) ◽  
pp. 913-920 ◽  
Author(s):  
Sh. Payrovi ◽  
S. Babaei
Keyword(s):  
Commutative Ring ◽  
Noetherian Ring ◽  
Ordered Set ◽  
Ordered Sets ◽  
Finitely Generated ◽  
Multiplication Module ◽  
Totally Ordered Set

In this paper, we introduce the concept of 2-absorbing submodules as a generalization of 2-absorbing ideals. Let R be a commutative ring and M an R-module. A proper submodule N of M is called 2-absorbing if whenever a, b ∈ R, m ∈ M and abm ∈ N, then am ∈ N or bm ∈ N or ab ∈ N:RM. Let N be a 2-absorbing submodule of M. It is shown that N:RM is a 2-absorbing ideal of R and either Ass R(M/N) is a totally ordered set or Ass R(M/N) is the union of two totally ordered sets. Furthermore, it is shown that if M is a finitely generated multiplication module over a Noetherian ring R, and Ass R(M/N) a totally ordered set, then N is 2-absorbing whenever N:RM is a 2-absorbing ideal of R. Also, the 2-absorbing avoidance theorem is proved.

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