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Mathematics and Its Applications

Semigroups and Their Subsemigroup Lattices

Authors: Shevrin, L.N., Ovsyannikov, A.J.

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About this 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.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-94-015-8751-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-0-7923-4221-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-90-481-4749-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Semigroups and Their Subsemigroup Lattices
Authors
Series Title
Mathematics and Its Applications
Series Volume
379
Copyright
1996
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-8751-8
DOI
10.1007/978-94-015-8751-8
Hardcover ISBN
978-0-7923-4221-2
Softcover ISBN
978-90-481-4749-6
Edition Number
1
Number of Pages
XI, 380
Additional Information
Originally published in Russian
Topics