Strong Semilattices of Implicative Semigroups
Keyword(s):
It is well known that a strong semilattice of semigroups is still a semigroup. However, it is not known whether the analogous result carries or not for a strong semilattice of implicative semigroups. The main difficulty is that the implicative operation ∗ is hard to define on the semilattice, especially we need the operation ∗ of the implicative semigroup to be compatible with the negatively ordered relation and the semigroup multiplication on the semilattice of implicative semigroups. In this paper, we provide a practical method of constructing such a strong semilattice of mplicative semigroups. Our method is particularly useful in constructing implicative semigroups of large size. A constructed example is given.
1977 ◽
Vol 71
(2)
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pp. 477-485
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2016 ◽
Vol 3
(1)
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1983 ◽
Vol 41
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pp. 244-245
Keyword(s):
1978 ◽
Vol 36
(1)
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pp. 176-177
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1994 ◽
Vol 52
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pp. 900-901