Relatively free *-bands

• Tipo: Artigo em Revista Científica Internacional
• Data: 2000

Autores

Petrich, M (Autor) Outra; Pedro V. Silva (Autor) FCUP

Revista

Título: Beitrage zur Algebra und Geometrie

Vol. 41 Nº 2

Páginas: 569-588

ISSN: 0138-4821

Editora: Springer Nature

Indexação

Scopus - 2 Citações

Outras Informações

ID Authenticus: P-009-KDZ

Abstract (EN): A *-band is an algebra consisting of a band (idempotent semigroup) on which an involution * is defined satisfying an extra condition; in summary (xy)* = y*x*, x** = x, x = xx*x, (xy)z = x(yz), x2 = x. The lattice of all *-band varieties was determined by Adair who also provided a basis for the identities of each variety. Another system of bases was devised by Petrich. Defining certain operators on the free involutorial semigroup F on a nonempty set X, we construct a system of fully invariant congruences on F which is in bijection with the set of all proper *-band varieties, with the exception of normal *-band varieties which require a different treatment. The proof of this result is based on those evoked above and is broken into a long sequence of lemmas. © 2000 Heldermann Verlag.

Idioma: Inglês

Tipo (Avaliação Docente): Científica