互结合性与三元二重半群
Interassociativity and three-element doppelsemigroups
摘要：
本文刻画了某些非逆半群的所有关联，刻画了三元（强）二重半群及其自同构群的同构。证明了存在$75$两两非同构的三元二重半群，其中$41$二重半群是交换的.非交换二重半群被划分为对偶二重半群的$17$对。在同构下还存在$3$阶的$65$强二重半群，并且所有非强二重半群都不是交换的.
英文摘要：
In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist $75$ pairwise non-isomorphic three-element doppelsemigroups among which $41$ doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into $17$ pairs of dual doppelsemigroups. Also up to isomorphism there are $65$ strong doppelsemigroups of order $3$, and all non-strong doppelsemigroups are not commutative.
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