1,264 research outputs found
Finite symmetric functions with non-trivial arity gap
Given an -ary
valued function , denotes the essential arity gap of
which is the minimal number of essential variables in which become fictive
when identifying any two distinct essential variables in . In the present
paper we study the properties of the symmetric function with non-trivial arity
gap (). We prove several results concerning decomposition of the
symmetric functions with non-trivial arity gap with its minors or subfunctions.
We show that all non-empty sets of essential variables in symmetric functions
with non-trivial arity gap are separable.Comment: 12 page
M-Solid Subvarieties of some Varieties of Commutative Semigroups
∗ 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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