Lattices embeddable in subsemigroup lattices. II. Cancellative semigroups |
| |
Authors: | M. V. Semenova |
| |
Affiliation: | (1) Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia |
| |
Abstract: | Repnitskii proved that any lattice embeds in a subsemigroup lattice of some commutative, cancellative, idempotent free semigroup with unique roots. In that proof, use is made of a result by Bredikhin and Schein stating that any lattice embeds in a suborder lattice of suitable partial order. Here, we present a direct proof of Repnitskii’s result which is independent of Bredikhin-Schein’s, thus giving the answer to the question posed by Shevrin and Ovsyannikov. Supported by INTAS grant No. 03-51-4110; RF Ministry of Education grant No. E02-1.0-32; Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2112.2003.1; a grant from the Russian Science Support Foundation; SB RAS Young Researchers Support project No. 11. __________ Translated from Algebra i Logika, Vol. 45, No. 4, pp. 436–446, July–August, 2006. |
| |
Keywords: | commutative semigroup subsemilattice lattice |
本文献已被 SpringerLink 等数据库收录! |
|