Monogenic free inverse semigroups and partial automorphisms of regular rooted trees

Q3 Mathematics Matematychni Studii Pub Date : 2024-03-19 DOI:10.30970/ms.61.1.3-9
E. Kochubinska, A. Oliynyk
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引用次数: 0

Abstract

For a one-to-one partial mapping on an infinite set, we present a criterion in terms of its cycle-chain decomposition that the inverse subsemigroup generated by this mapping is monogenic free inverse. We also give a sufficient condition for a regular rooted tree partial automorphism to extend to a partial automorphism of another regular rooted tree so that the inverse semigroup gene\-ra\-ted by this extended partial automorphism is monogenic free inverse. The extension procedure we develop is then applied to $n$-ary adding machines.
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规则有根树的单原自由逆半群和部分自动形态
对于无穷集上的一对一局部映射,我们根据其循环链分解提出了一个标准,即该映射产生的逆子半群是单源自由逆。我们还给出了一个充分条件,即有规则有根树的部分自动形可以扩展为另一个有规则有根树的部分自动形,从而由这个扩展的部分自动形生成的逆子半群是单源自由逆。我们开发的扩展程序随后被应用于 $n$ary 加法器。
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来源期刊
Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
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