Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
A Lattice Isomorphism Theorem for Nonsingular Retractable Modules
View through CrossRef
AbstractLet RM be a nonsingular module such that B = EndR(M) is left nonsingular and has as its maximal left quotient ring, where is the injective hull of RM. Then it is shown that there is a lattice isomorphism between the lattice C(M) of all complement submodules of RM and the lattice C(B) of all complement left ideals of B, and that RM is a CS module if and only if B is a left CS ring. In particular, this is the case if RM is nonsingular and retractable.
Title: A Lattice Isomorphism Theorem for Nonsingular Retractable Modules
Description:
AbstractLet RM be a nonsingular module such that B = EndR(M) is left nonsingular and has as its maximal left quotient ring, where is the injective hull of RM.
Then it is shown that there is a lattice isomorphism between the lattice C(M) of all complement submodules of RM and the lattice C(B) of all complement left ideals of B, and that RM is a CS module if and only if B is a left CS ring.
In particular, this is the case if RM is nonsingular and retractable.
Related Results
Boundary Spanning and Isomorphism Interactions
Boundary Spanning and Isomorphism Interactions
This study explores the relationship between isomorphism, boundary-spanning, institutional restrictions, and procedural congruence. Using fuzzy (set-theoretic) logic and concepts o...
ON A MODULE CONTAINING A COPY OF ITS FACTOR BY A $t$-CLOSED SUBMODULE
ON A MODULE CONTAINING A COPY OF ITS FACTOR BY A $t$-CLOSED SUBMODULE
In this paper, we introduce the notion of $t$-co-epi-retractable as generalization of $c$-co-epi-retractable. An $R$-module $M$ is called $t$-co-epi-retractable if contains a copy ...
Isomorphism on Complex Fuzzy Graph
Isomorphism on Complex Fuzzy Graph
Objective: To investigate isomorphism between two complex fuzzy graphs and prove it is an equivalence relation. The major objective of this research paper is to elucidate weak and ...
Semi-Small Compressible Modules and Semi-Small Retractable Modules
Semi-Small Compressible Modules and Semi-Small Retractable Modules
Let be a commutative ring with 1 and be left unitary . In this paper we introduced and studied concept of semi-small compressible module (a is said to be semi-small compress...
SUBATOMIC: a SUbgraph BAsed mulTi-OMIcs clustering framework to analyze integrated multi-edge networks
SUBATOMIC: a SUbgraph BAsed mulTi-OMIcs clustering framework to analyze integrated multi-edge networks
Abstract
Background
Representing the complex interplay between different types of biomolecules across different omics lay...
SUBATOMIC: a SUbgraph BAsed mulTi-OMIcs Clustering framework to analyze integrated multi-edge networks
SUBATOMIC: a SUbgraph BAsed mulTi-OMIcs Clustering framework to analyze integrated multi-edge networks
Abstract
Representing the complex interplay between different types of biomolecules across different omics layers in multi-omics networks bears great potential to g...
Isomorphism
Isomorphism
Abstract
Isomorphism refers to the process whereby organizations become increasingly similar over time. There are two main approaches to understanding isomorphism: compet...
Design and control of large-detuned optical lattice based on 87Rb atoms
Design and control of large-detuned optical lattice based on 87Rb atoms
An innovative and practical scheme of building far-detuned optical lattice for 87Rb atoms is proposed.The disposals of aligning the lattice beams,tuning the lattice frequency and c...