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Vietnam Journal of Mathematics 35:4(2007)
495-505
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Finite Semigroups with Infinite Product and
Languages of Infinite Words
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Phan Trung Huy,
Nguyen Quy Khang, and Do Long Van
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Abstract. A semigroup (monoid) S, which can be equipped with an
infinite product compatible with the given multiplication in $S$, is called
a semigroup (monoid, resp.) with infinite product (abbreviated by SWIP and
MWIP, resp.). In this paper, necessary and sufficient conditions for a finite
semigroup to be a SWIP are established. Relationships between MWIPs and
varieties of finite monoids, and also between MWIPs and regular languages
of infinite words are considered.
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2000 Mathematics Subject Classification: 20M35, 20M07,
68Q45, 68Q68.
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Keywords: Semigroup, monoid, infinite product,
variety of finite monoids, $\omega$-language.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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