caa a22 4500 467899738 CHVBK 20180406152814.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s00012-006-1989-6 doi (NATIONALLICENCE)springer-10.1007/s00012-006-1989-6 Wismath Shelly Dept. of Mathematics and Computer Science, University of Lethbridge, T1K-3M4, Lethbridge, Alberta, Canada aut Hyperidentities and solid varieties [Elektronische Daten] [Shelly Wismath] Abstract.: Let V be a variety of type τ. A type τ hyperidentity of V is an identity of V which also holds in an additional stronger sense: for every substitution of terms of the variety (of appropriate arity) for the operation symbols in the identity, the resulting equation holds as an identity of the variety. Such identities were first introduced by Walter Taylor in [27] in 1981. A variety is called solid if all its identities also hold as hyperidentities. For example, the semigroup variety of rectangular bands is a solid variety. For any fixed type τ, the collection of all solid varieties of type τ forms a complete lattice which is a sublattice of the lattice L(τ) of all varieties of type τ. In this paper we give an overview of the study of hyperidentities and solid varieties, particularly for varieties of semigroups, culminating in the construction of an infinite collection of solid varieties of arbitrary type. Birkhäuser Verlag, Basel, 2007 Identity nationallicence hyperidentity nationallicence solid variety nationallicence varieties of semigroups nationallicence algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/2-3(2006-08-01), 305-318 0002-5240 55:2-3<305 2006 55 12 https://doi.org/10.1007/s00012-006-1989-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00012-006-1989-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wismath Shelly Dept. of Mathematics and Computer Science, University of Lethbridge, T1K-3M4, Lethbridge, Alberta, Canada aut NATIONALLICENCE 773 0- algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/2-3(2006-08-01), 305-318 0002-5240 55:2-3<305 2006 55 12 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer