Semigroups and Their Subsemigroup Lattices

di L.N. Shevrin (Autore)

A.J. Ovsyannikov (Autore)

Springer, 2010

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.

• Autore: L.N. Shevrin, A.J. Ovsyannikov
• Editore: Springer
• Collana: Mathematics and Its Applications
• Anno: 2010
• Rilegatura: Paperback / softback
• Pagine: 380 p.
• Dimensioni: 235 x 155 mm
• EAN: 9789048147496

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