1,300 research outputs found
Indispensable binomials in semigroup ideals
In this paper, we deal with the problem of uniqueness of minimal system of
binomial generators of a semigroup ideal. Concretely, we give different
necessary and/or sufficient conditions for uniqueness of such minimal system of
generators. These conditions come from the study and combinatorial description
of the so-called indispensable binomials in the semigroup ideal.Comment: 11 pages. This paper was initially presented at the II Iberian
Mathematical Meeting (http://imm2.unex.es). To appear in the Proc. Amer.
Math. So
Unary enhancements of inherently nonfinitely based semigroups
We exhibit a simple condition under which a finite involutary semigroup whose
semigroup reduct is inherently nonfinitely based is also inherently nonfinitely
based as a unary semigroup. As applications, we get already known as well as
new examples of inherently nonfinitely based involutory semigroups. We also
show that for finite regular semigroups, our condition is not only sufficient
but also necessary for the property of being inherently nonfinitely based to
persist. This leads to an algorithmic description of regular inherently
nonfinitely based involutory semigroups.Comment: 11 pages, 1 figure. Section 4 has been improved and expanded
according to suggestions of an anonymous referee of the journal version. A
few minor improvements have been done in Section
Approximate Homomorphisms of Ternary Semigroups
A mapping between ternary semigroups will be
called a ternary homomorphism if . In this paper,
we prove the generalized Hyers--Ulam--Rassias stability of mappings of
commutative semigroups into Banach spaces. In addition, we establish the
superstability of ternary homomorphisms into Banach algebras endowed with
multiplicative norms.Comment: 10 page
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