On generating countable sets of endomorphisms

J Araujo; James David Mitchell; N Silva

doi:10.1007/s00012-003-1809-1

On generating countable sets of endomorphisms

Research output: Contribution to journal › Article › peer-review

Abstract

Sierpinski proved that every countable set of mappings on an infinite set X is contained in a 2-generated subsemigroup of the semigroup of all mappings on X. In this paper we prove that every countable set of endomorphisms of an algebra A which has an infinite basis (independent generating set) is contained in a 2-generated subsemigroup of the semigroup of all endomorphisms of A.

Original language	English
Pages (from-to)	61-67
Number of pages	7
Journal	Algebra Universalis
Volume	50
Issue number	1
DOIs	https://doi.org/10.1007/s00012-003-1809-1
Publication status	Published - 2003

Keywords

endomorphisms
universal algebras
independence
semigroups
INDEPENDENCE ALGEBRA
IDEMPOTENT ENDOMORPHISMS
FINITE RANK
PRODUCTS

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10.1007/s00012-003-1809-1

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AU - Silva, N

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KW - endomorphisms

KW - universal algebras

KW - independence

KW - semigroups

KW - INDEPENDENCE ALGEBRA

KW - IDEMPOTENT ENDOMORPHISMS

KW - FINITE RANK

KW - PRODUCTS

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JO - Algebra Universalis

JF - Algebra Universalis

IS - 1

ER -

On generating countable sets of endomorphisms

Abstract

Keywords

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