Polynomial density of commutative semigroups
1993 ◽
Vol 48
(1)
◽
pp. 151-162
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Keyword(s):
An algebra is said to be polynomially n−dense if all equational theories extending the equational theory of the algebra with constants have a relative base consisting of equations in no more than n variables. In this paper, we investigate polynomial density of commutative semigroups. In particular, we prove that, for n > 1, a commutative semigroup is (n − 1)-dense if and only if its subsemigroup consisting of all n−factor-products is either a monoid or a union of groups of a bounded order. Moreover, a commutative semigroup is 0-dense if and only if it is a bounded semilattice. For semilattices, we give a full description of the corresponding lattices of equational theories.
1992 ◽
Vol 34
(2)
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pp. 133-141
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2008 ◽
Vol 145
(3)
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pp. 579-586
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Keyword(s):
1990 ◽
Vol 108
(3)
◽
pp. 429-433
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2003 ◽
Vol 356
(9)
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pp. 3483-3504
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Keyword(s):
2021 ◽
Vol 12
(3)
◽
pp. 5150-5155
Keyword(s):