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Karl Auinger, Igor Dolinka, Michael V. Volkov (2012)
Journal of the European Mathematical Society
We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.
Ilinka Dimitrova, Jörg Koppitz (2006)
Discussiones Mathematicae - General Algebra and Applications
For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type τ...
Edmond W. H. Lee, Jian Rong Li (2011)
P.R. Jones (1993)
Semigroup forum
Paul Blanchard (1991)
Semigroup forum
Koppitz, J. (1997)
Serdica Mathematical Journal
∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent.
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