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Semigroups and Their Subsemigroup Lattices

Semigroups and Their Subsemigroup Lattices


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About the Book

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.


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Product Details
  • ISBN-13: 9789048147496
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: Softcover reprint of hardcover 1st ed. 1996
  • Language: English
  • Returnable: Y
  • Spine Width: 21 mm
  • Width: 156 mm
  • ISBN-10: 9048147492
  • Publisher Date: 15 Dec 2010
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 380
  • Series Title: Mathematics and Its Applications
  • Weight: 603 gr


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