Bibliographic Information

Semigroups and their subsemigroup lattices

by L.N. Shevrin and A.J. Ovsyannikov

(Mathematics and its applications, v. 379)

Kluwer, c1996

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Note

Includes bibliographical references and index

Description and Table of Contents

Description

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.

Table of Contents

Preface. Part A: 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. Part B: Properties of Subsemigroup Lattices. VII. Lattice Characteristics of Classes of Semigroups. VIII. Embedding Lattices in Subsemigroup Lattices. Part 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. Bibliography. Index. List of Notations. List of Subsections Containing Unsolved Problems or Open Questions.

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Details

  • NCID
    BA28824515
  • ISBN
    • 0792342216
  • LCCN
    96033294
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht ; Boston
  • Pages/Volumes
    xi, 378 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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