A numerical semigroup is a subset S of N such that is closed under sums, contains the zero and generates Z as a group. From this definition Ž w x. Ž one obtains see, for example, 2 that S has a conductor C i.e., the . maximum among all the natural numbers not belonging to S . A numerical semigroup S is called symmetric if for every integer z f S, C y z g S. The study of the subsemigroups of N i...

A $C$-semigroup (respectively a $D$-semigroup) is positioned numerical semigroup $S$ such that $\rm{g}(S)=\frac{\rm{F}(S)+\rm{m}(S)-1}{2}$ $\rm{g}(S)=\frac{\rm{F}(S)+\rm{m}(S)-2}{2}$). In this paper we study these semigroups giving formulas for the Frobenius number, pseudo-Frobenius and type. Furthermore, give algorithms computing whole set of $C$-semigroups $D$-semigroups.

It is known that every semigroup of normal completely positive maps P = {Pt : t ≥ 0} of B(H), satisfying Pt(1) = 1 for every t ≥ 0, has a minimal dilation to an E0-semigroup acting on B(K) for some Hilbert space K ⊇ H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the ind...

A numerical semigroup $S$ is an additive subsemigroup of the non-negative integers with finite complement, and squarefree divisor complex element $m \in S$ a simplicial $\Delta_m$ that arises in study multigraded Betti numbers. We compute complexes for certain classes semigroups, exhibit new family are occur as some element.

Ulrich ideals in numerical semigroup rings of small multiplicity are studied. If the semigroups three-generated but not symmetric, Golod, since Betti numbers residue class fields form an arithmetic progression; therefore, these G-regular ([15]), possessing no ideals. Nevertheless, even case, situation is different, when symmetric. We shall explore this phenomenon, describing explicit system gen...

We provide an expression for the conductor \(c(\varDelta )\) of a semimodule \(\varDelta \) numerical semigroup \(\varGamma with two generators in terms syzygy module and semigroup. In particular, we deduce that difference between is element \), as well formula dual \).