Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111252
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dc.contributor.authorOvsyannikov, A. Ya.en
dc.date.accessioned2022-05-12T08:15:24Z-
dc.date.available2022-05-12T08:15:24Z-
dc.date.issued2020-
dc.identifier.citationOvsyannikov 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.en
dc.identifier.issn0134-4889-
dc.identifier.otherAll Open Access, Bronze3
dc.identifier.urihttp://hdl.handle.net/10995/111252-
dc.description.abstractLet 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.en
dc.format.mimetypeapplication/pdfen
dc.language.isoruen
dc.publisherKrasovskii Institute of Mathematics and Mechanicsen1
dc.publisherKrasovskii Institute of Mathematics and Mechanics UB RASen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceTr. Inst. Mat. Meh. UrO RAN2
dc.sourceTrudy Instituta Matematiki i Mekhaniki UrO RANen
dc.subject1-LATTICE ISOMORPHISMen
dc.subjectFREE PRODUCTen
dc.subjectMONOIDen
dc.subjectSUBMONOID LATTICEen
dc.title1-Lattice Isomorphisms of Monoids Decomposable Into a Free Producten
dc.title.alternative1-решеточные изоморфизмы моноидов, разложимых в свободное произведениеru
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.scopus85095702556-
local.contributor.employeeOvsyannikov, A.Ya., Department of Mathematics, Mechanics and Computer Science, Ural Federal University, Yekaterinburg, 620083, Russian Federationen
local.description.firstpage142-
local.description.lastpage153-
local.issue3-
local.volume26-
local.contributor.departmentDepartment of Mathematics, Mechanics and Computer Science, Ural Federal University, Yekaterinburg, 620083, Russian Federationen
local.identifier.pure13944431-
local.identifier.eid2-s2.0-85095702556
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