883 research outputs found
Structure of Chinese algebras
The structure of the algebra K[M] of the Chinese monoid M over a field K is
studied. The minimal prime ideals are described. They are determined by certain
homogeneous congruences on M and they are in a one to one correspondence with
diagrams of certain special type. There are finitely many such ideals. It is
also shown that the prime radical B(K[M]) of K[M] coincides with the Jacobson
radical and the monoid M embeds into the algebra K[M]/B(K[M]). A new
representation of M as a submonoid of the direct product of finitely many
copies of the bicyclic monoid and finitely many copies of the infinite cyclic
monoid is derived. Consequently, M satisfies a nontrivial identity
Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then construct biautomatic structures. For hypoplactic monoids, we construct finite complete rewriting systems and biautomatic structures. For sylvester monoids, which are not finitely presented, we prove that the standard presentation is an infinite complete rewriting system, and construct biautomatic structures. Consequently, the monoid algebras corresponding to monoids of these classes are automaton algebras in the sense of Ufnarovskij
A construction of integer-valued polynomials with prescribed sets of lengths of factorizations
For an arbitrary finite set S of natural numbers greater 1, we construct an
integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of
lengths of f is the set of all natural numbers n, such that f has a
factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z)
contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page
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