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 H is not symmetric and assume that the definig ideal of R is defined by maximal minorsThen 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 give Frobenius number.

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The notion of Ulrich ideals was introduced by Goto et al. [3]. They developed an interesting theory on Ulrich ideals. In particular, they gave a characterization of Ulrich ideals of Gorenstein numerical semigroup rings that are generated by monomials. Using this result, in this paper, we investigate Ulrich ideals of Gorenstein numerical semigroup rings with embedding dimension 3 that are generated by monomials. In particular, we completely determine when such Ulrich ideals are existent in those rings. 2010 AMS Mathematics subject classification. Primary 13H10, 20M14, 20M25.