Image partition regularity of matrices over commutative semigroups

2019 ◽  
Vol 259 ◽  
pp. 179-202
Author(s):  
Neil Hindman ◽  
Dona Strauss
Keyword(s):  
Commutative Semigroups ◽  
Image Partition

scholarly journals Commutative semigroups whose endomorphisms are power functions

2021 ◽  
Author(s):  
Ryszard Mazurek
Keyword(s):  
Positive Integer ◽  
Power Function ◽  
Cyclic Group ◽  
Commutative Semigroup ◽  
Commutative Monoid ◽  
Power Functions ◽  
Commutative Semigroups ◽  
Finite Cyclic Group

AbstractFor any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ f : S → S defined by $$f(x) = x^m$$ f ( x ) = x m is an endomorphism of S. We partly solve the Lesokhin–Oman problem of characterizing the commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid S is a power function if and only if S is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup S with an idempotent is a power function if and only if S is a finite cyclic semigroup. Furthermore, we prove that every endomorphism of a nontrivial commutative atomic monoid S with 0, preserving 0 and 1, is a power function if and only if either S is a finite cyclic group with zero adjoined or S is a cyclic nilsemigroup with identity adjoined. We also prove that every endomorphism of a 2-generated commutative semigroup S without idempotents is a power function if and only if S is a subsemigroup of the infinite cyclic semigroup.

Some quasi-ordered classes of finite commutative semigroups

1985 ◽  
Vol 32 (1) ◽  
pp. 189-200
Author(s):  
Jorge Almeida
Keyword(s):  
Commutative Semigroups

Quasi commutative semigroups and σ-reflexive semigroups

1980 ◽  
Vol 19 (1) ◽  
pp. 313-321 ◽  
Author(s):  
A. Cherubini Spoletini ◽  
A. Varisco
Keyword(s):  
Commutative Semigroups

On lattice-ordered commutative semigroups

2003 ◽  
Vol 50 (3-4) ◽  
pp. 341-357 ◽  
Author(s):  
Laszlo Fuchs ◽  
Raquel Reis
Keyword(s):  
Commutative Semigroups
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