ScholarLens Back to search
1972•Transactions of the American Mathematical SocietyOpen access

The Study of Commutative Semigroups with Greatest Group-Homomorphism

Takayuki Tamura, Howard B. Hamilton

Open full text 5 citations

Abstract

This paper characterizes commutative semigroups which admit a greatest group-homomorphism in various ways. One of the important theorems is that a commutative semigroup $S$ has a greatest group-homomorphic image if and only if for every $a \in S$ there are $b,c \in S$ such that $abc = c$. Further the authors study a relationship between $S$ and a certain cofinal subsemigroup and discuss the structure of commutative separative semigroups which have a greatest group-homomorphic image.

Open-access reader

About this research paper

What this paper is about

This paper characterizes commutative semigroups which admit a greatest group-homomorphism in various ways. One of the important theorems is that a commutative semigroup $S$ has a greatest group-homomorphic image if and only if for every $a \in S$ there are $b,c \in S$ such that $abc = c$. Further the authors study a relationship between $S$ and a certain cofinal subsemigroup and discuss the structure of commutative separative semigroups which have a greatest group-homomorphic image.

Why it matters

OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

This paper characterizes commutative semigroups which admit a greatest group-homomorphism in various ways. One of the important theorems is that a commutative semigroup $S$ has a greatest group-homomorphic image if and only if for every $a \in S$ there are $b,c \in S$ such that $abc = c$. Further the authors study a relationship between $S$ and a certain cofinal subsemigroup and discuss the structure of commutative separative semigroups which have a greatest group-homomorphic image.

Key concepts: Homomorphism, Mathematics, Commutative property, Semigroup, Homomorphic encryption, Group (periodic table), Image (mathematics), Pure mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The Study of Commutative Semigroups with Greatest Group-Homomorphism — Research Paper | ScholarLens