Memoirs of the Faculty of Science, Shimane University

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Memoirs of the Faculty of Science, Shimane University 23
1989-12-25 発行

完全正則半群の部分直積について2,3の注意

Some Remarks on Subdirect Products of Compretely Regular Semigroups
Yamada, Miyuki
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Description
In this paper, the concept of a subspined product of completely regular semigroups are introduced. Firstly, we give a necessary and sufficient condition for a subspined product A[#45度]B of cryptogroups A and B to be also a cryptogroup. Secondly, it is shown that a subspined product A [#45度] B is necessarily a cryptogroup if one of A and B is a band and the other is a cryptogroup. It is also shown that any subspined product A ~ B coincides with the spined product A 〓 B if one of A and B is a Clifford semrgroup and the other is a band.
Finally, the concept of a subspined product is extended to the concept of a P-subspined product for the class of completely P-regular semigroups, and some considerations are given for P-subspined products of P-cryptogroups.