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Overview0.1. 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. Full Product DetailsAuthor: L.N. Shevrin , A.J. OvsyannikovPublisher: Springer Imprint: Springer Edition: 1996 ed. Volume: 379 Dimensions: Width: 15.60cm , Height: 2.20cm , Length: 23.40cm Weight: 1.610kg ISBN: 9780792342212ISBN 10: 0792342216 Pages: 380 Publication Date: 31 October 1996 Audience: College/higher education , General/trade , Professional and scholarly , Undergraduate , General Format: Hardback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsA. Semigroups with Certain Types of Subsemigroup Lattices.- I. Preliminaries.- II. Semigroups with Modular or Semimodular Subsemigroup Lattices.- III. Semigroups with Complementable Subsemigroups.- IV. Finiteness Conditions.- V. Inverse Semigroups with Certain Types of Lattices of Inverse Subsemigroups.- VI. Inverse Semigroups with Certain Types of Lattices of Full Inverse Subsemigroups.- B. Properties of Subsemigroup Lattices.- VII. Lattice Characteristics of Classes of Semigroups.- VIII. Embedding Lattices in Subsemigroup Lattices.- C. Lattice Isomorphisms.- IX. Preliminaries on Lattice Isomorphisms.- X. Cancellative Semigroups.- XI. Commutative Semigroups.- XII. Semigroups Decomposable into Rectangular Bands.- XIII. Semigroups Defined by Certain Presentations.- XIV. Inverse Semigroups.- List of Notations.- List of Subsections Containing Unsolved Problems or Open Questions.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |