ON THE NUMBER OF SUBSEMIGROUPS OF DIRECT PRODUCTS INVOLVING THE FREE MONOGENIC SEMIGROUP
2019 ◽
Vol 109
(1)
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pp. 24-35
Keyword(s):
The direct product $\mathbb{N}\times \mathbb{N}$ of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for $\mathbb{N}\times S$, where $S$ is a finite semigroup. It contains only countably many pairwise nonisomorphic subsemigroups if and only if $S$ is a union of groups. And it contains only countably many pairwise nonisomorphic subdirect products if and only if every element of $S$ has a relative left or right identity element.
1982 ◽
Vol 92
(3-4)
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pp. 301-317
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Keyword(s):
Keyword(s):
1980 ◽
Vol 85
(3-4)
◽
pp. 337-351
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2001 ◽
Vol 44
(2)
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pp. 379-388
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Keyword(s):
1966 ◽
Vol 18
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pp. 1004-1014
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1990 ◽
Vol 48
(1)
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pp. 87-88
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1983 ◽
Vol 26
(2)
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pp. 233-240
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1960 ◽
Vol 12
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pp. 447-462
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