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REMARKS ON DIRECT PRODUCTS OF COMMUTATIVE SEMIGROUPS

ALFRED TARSKI
Mathematica Scandinavica
Vol. 5, No. 2 (April 15, 1958), pp. 218-223
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24490314
Page Count: 6
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REMARKS ON DIRECT PRODUCTS OF COMMUTATIVE SEMIGROUPS
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Abstract

It is shown that with every Boolean algebra 𝔄 a commutative semigroup (i.e., a commutative and associative system with the cancellation law) 𝔄* can be correlated in such a way that, for any Boolean algebras 𝔄 and 𝔅, the formulas 𝔄 ≅ 𝔅 and 𝔄* ≅ 𝔅* are equivalent, and the formula (𝔄 × 𝔅)* ≅ 𝔄* × 𝔅* holds. In consequence, the results established in the preceding note of Hanf, On some fundamental problems concerning isomorphism of Boolean algebras [Math. Scand. 5 (1957), 205–217], can be extended from Boolean algebras to commutative semigroups.

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