Homomorphisms of Product Semigroups

Henrik Stetkær

doi:10.1007/s00025-022-01603-w

Homomorphisms of Product Semigroups

^*Corresponding author for this work

Department of Mathematics

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5 Citations (Scopus)

Abstract

Let S₁, ⋯ , S_N and R be semigroups. For homomorphisms F: S₁× ⋯ × S_N→ R we derive sufficient conditions for existence and uniqueness of homomorphisms F_n: S_n→ R, n= 1 , ⋯ , N, such that F(s₁, ⋯ , s_N) = F₁(s₁) ⋯ F_N(s_N) for all s₁∈ S₁, ⋯ , s_N∈ S_N.

Original language	English
Article number	60
Journal	Results in Mathematics
Volume	77
Issue	2
ISSN	1422-6383
DOIs	https://doi.org/10.1007/s00025-022-01603-w
Publication status	Published - Apr 2022

Keywords

decomposition
homomorphism
product semigroup
Semigroup

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10.1007/s00025-022-01603-w

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title = "Homomorphisms of Product Semigroups",

abstract = "Let S1, ⋯ , SN and R be semigroups. For homomorphisms F: S1× ⋯ × SN→ R we derive sufficient conditions for existence and uniqueness of homomorphisms Fn: Sn→ R, n= 1 , ⋯ , N, such that F(s1, ⋯ , sN) = F1(s1) ⋯ FN(sN) for all s1∈ S1, ⋯ , sN∈ SN.",

keywords = "decomposition, homomorphism, product semigroup, Semigroup",

author = "Henrik Stetk{\ae}r",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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language = "English",

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T1 - Homomorphisms of Product Semigroups

AU - Stetkær, Henrik

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N2 - Let S1, ⋯ , SN and R be semigroups. For homomorphisms F: S1× ⋯ × SN→ R we derive sufficient conditions for existence and uniqueness of homomorphisms Fn: Sn→ R, n= 1 , ⋯ , N, such that F(s1, ⋯ , sN) = F1(s1) ⋯ FN(sN) for all s1∈ S1, ⋯ , sN∈ SN.

AB - Let S1, ⋯ , SN and R be semigroups. For homomorphisms F: S1× ⋯ × SN→ R we derive sufficient conditions for existence and uniqueness of homomorphisms Fn: Sn→ R, n= 1 , ⋯ , N, such that F(s1, ⋯ , sN) = F1(s1) ⋯ FN(sN) for all s1∈ S1, ⋯ , sN∈ SN.

KW - decomposition

KW - homomorphism

KW - product semigroup

KW - Semigroup

UR - http://www.scopus.com/inward/record.url?scp=85122934014&partnerID=8YFLogxK

U2 - 10.1007/s00025-022-01603-w

DO - 10.1007/s00025-022-01603-w

M3 - Journal article

AN - SCOPUS:85122934014

SN - 1422-6383

VL - 77

JO - Results in Mathematics

JF - Results in Mathematics

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M1 - 60

ER -

Homomorphisms of Product Semigroups

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Keywords

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