无非重要有限子群的正统半群的晶格同构

IF 0.7 3区数学 Q2 MATHEMATICS

Semigroup Forum Pub Date : 2024-04-16 DOI:10.1007/s00233-024-10428-8

Simon M. Goberstein

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引用次数: 0

摘要

如果两个半群的子半群网格是同构的，那么这两个半群就是网格同构的；如果一个半群类包含了与该类中某个半群网格同构的每个半群，那么这个半群类就是网格封闭的。一个正交半群是一个正则半群，它的幂等子构成一个子半群。我们证明，所有没有非琐有限子群的正交半群类都是晶格封闭的。

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Lattice isomorphisms of orthodox semigroups with no nontrivial finite subgroups

Two semigroups are lattice isomorphic if their subsemigroup lattices are isomorphic, and a class of semigroups is lattice closed if it contains every semigroup which is lattice isomorphic to some semigroup from that class. An orthodox semigroup is a regular semigroup whose idempotents form a subsemigroup. We prove that the class of all orthodox semigroups having no nontrivial finite subgroups is lattice closed.

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来源期刊

Semigroup Forum 数学-数学

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

12 months

期刊介绍： Semigroup Forum is a platform for speedy and efficient transmission of information on current research in semigroup theory. Scope: Algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, numerical semigroups, transformation semigroups, semigroups of operators, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, logic, etc. Languages: English (preferred), French, German, Russian. Survey Articles: Expository, such as a symposium lecture. Of any length. May include original work, but should present the nonspecialist with a reasonably elementary and self-contained account of the fundamental parts of the subject. Research Articles: Will be subject to the usual refereeing procedure. Research Announcements: Description, limited to eight pages, of new results, mostly without proofs, of full length papers appearing elsewhere. The announcement must be accompanied by a copy of the unabridged version. Short Notes: (Maximum 4 pages) Worthy of the readers'' attention, such as new proofs, significant generalizations of known facts, comments on unsolved problems, historical remarks, etc. Research Problems: Unsolved research problems. Announcements: Of conferences, seminars, and symposia on Semigroup Theory. Abstracts and Bibliographical Items: Abstracts in English, limited to one page, of completed work are solicited. Listings of books, papers, and lecture notes previously published elsewhere and, above all, of new papers for which preprints are available are solicited from all authors. Abstracts for Reviewing Journals: Authors are invited to provide with their manuscript informally a one-page abstract of their contribution with key words and phrases and with subject matter classification. This material will be forwarded to Zentralblatt für Mathematik.