Semigroups and Their Subsemigroup Lattices: 379 (Mathematics and Its Applications, 379) - Image 1

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Springer Semigroups and Their Subsemigroup Lattices: 379 (Mathematics and Its Applications, 379)

Name: Semigroups and Their Subsemigroup Lattices: 379 (Mathematics and Its Applications, 379)
Brand: Springer
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Algebra

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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.

Product Specifications

Brand: Springer
Format: hardcover
ASIN: 0792342216
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 31 October 1996
Listed Since: 18 December 2006

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Springer Semigroups and Their Subsemigroup Lattices: 379 (Mathematics and Its Applications, 379)

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