Binomial semigroups
A binomial semigroup is a semigroup with a finite set \(x_1,\dots,x_n\) of generators subject to \(\frac{n(n-1)}2\) relations of the type \(x_jx_i=x_kx_l\) with \(j>i\), \(k<l\), \(k<j\). These semigroups were studied by Gateva-Ivanova and Van den Bergh in their investigations of skew polynomial rings. From the authors abstract: ``In this paper we study the structure of binomial semigroups and investigate the height one prime ideals of their binomial skew polynomial rings. In particular, we give a representation theorem of such semigroups as a product of binomial semigroups of fewer generators and we prove that binomial semigroups have (torsion-free) solvable groups of quotients. It is shown that binomial semigroups are Noetherian maximal orders in their quotient group and have trivial normalizing class group. Quotient rings and localizations with respect to height one primes of the binomial skew polynomial ring are described. It follows that binomial skew semigroup rings are Noetherian maximal orders with principal homogeneous height one prime ideals''.
scientific article; zbMATH DE number 1203895
scientific article