Semigroups and Their Subsemigroup Lattices (Hardcover, 1996 ed.)

0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book [Baer] was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 379
Release date:	2001
First published:	1996
Authors:	L. N Shevrin • A. J Ovsyannikov
Dimensions:	234 x 156 x 22mm (L x W x T)
Format:	Hardcover
Pages:	380
Edition:	1996 ed.
ISBN-13:	978-0-7923-4221-2
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
LSN:	0-7923-4221-6
Barcode:	9780792342212

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