Symmetric and Pseudo-Symmetric Numerical Semigroups via Young Diagrams and Their Semigroup Rings
J. Korean Math. Soc.
Published online July 29, 2021
Meral Suer and Mehmet Yesil
Batman University; Batman University
Abstract : This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric semigroups into an over semigroup and its dual. It is also given exactly for what kind of numerical semigroup S, the semigroup ring |[[S]] has at least one Gorenstein subring and has at least one Kunz subring.
Keywords : Symmetric numerical semigroups, Pseudo-symmetric numerical semigroups, Young diagrams, Semigroup rings
MSC numbers : 20M14, 20M20, 20M25
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