Please use this identifier to cite or link to this item: http://elar.urfu.ru/handle/10995/111252
Title: 1-Lattice Isomorphisms of Monoids Decomposable Into a Free Product
Other Titles: 1-решеточные изоморфизмы моноидов, разложимых в свободное произведение
Authors: Ovsyannikov, A. Ya.
Issue Date: 2020
Publisher: Krasovskii Institute of Mathematics and Mechanics
Krasovskii Institute of Mathematics and Mechanics UB RAS
Citation: Ovsyannikov A. Ya. 1-Lattice Isomorphisms of Monoids Decomposable Into a Free Product [1-решеточные изоморфизмы моноидов, разложимых в свободное произведение] / A. Ya. Ovsyannikov // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 3. — P. 142-153.
Abstract: Let M and M′ be monoids. Denote by Sub1M the lattice of all submonoids of M. Any isomorphism of Sub1M onto the lattice Sub1M′ is called a 1-lattice isomorphism of M onto M′. We say that a bijection ϕ of M onto M′ induces a 1-lattice isomorphism ψ of M onto M′ if ϕ(K) = ψ(K) for any submonoid K ∈ Sub1M. A monoid M is strictly 1-lattice determined if any of its 1-lattice isomorphisms onto an arbitrary monoid is induced either by an isomorphism or by an antiisomorphism. The similar notions of a group strictly determined by its subgroup lattice and a semigroup strictly determined by its subsemigroup lattice have long attracted attention and have been actively studied in the classes of groups and semigroups. For monoids almost nothing has been known here. However, the following question was asked about forty years ago: is any monoid that is decomposable into a free product strictly 1-lattice determined? A complete answer to this question is found. Namely, it is proved that an arbitrary monoid nontrivially decomposable into a free product is strictly 1-lattice determined. This result has something in common with the well-known results on the strictly lattice determinability of both a group nontrivially decomposable into a free product and a semigroup decomposable into a free product. © Krasovskii Institute of Mathematics and Mechanics.
Keywords: 1-LATTICE ISOMORPHISM
FREE PRODUCT
MONOID
SUBMONOID LATTICE
URI: http://elar.urfu.ru/handle/10995/111252
Access: info:eu-repo/semantics/openAccess
RSCI ID: 43893870
SCOPUS ID: 85095702556
PURE ID: 13944431
ISSN: 0134-4889
DOI: 10.21538/0134-4889-2020-26-3-142-153
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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