| Semigroups and Their Subsemigroup Lattices Contributor(s): Shevrin, L. N. (Author), Ovsyannikov, A. J. (Author) |
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ISBN: 9048147492 ISBN-13: 9789048147496 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Algebra - General - Mathematics | Logic |
| Dewey: 512.27 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.81" H x 6.14" W x 9.21" (1.21 lbs) 380 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |
