Article ID Journal Published Year Pages File Type
4585745 Journal of Algebra 2012 7 Pages PDF
Abstract

Let H=〈a,b,c〉 be a numerical semigroup generated by three elements and let R=k[H] be its semigroup ring over a field k. We assume that H is not symmetric and assume that the defining ideal of R is defined by maximal minors of the matrix . Then we will show that the genus of H is determined by the Frobenius number F(H) and αβγ or α′β′γ′. In particular, we show that H is pseudo-symmetric if and only if αβγ=1 or α′β′γ′=1.Also, we will give a simple algorithm to get all the pseudo-symmetric numerical semigroups H=〈a,b,c〉 with given Frobenius number.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory