For a numerical semigroup ring K[H] we study the trace of its canonical ideal. The colength this ideal is called residue H. This invariant measures how far H from being symmetric, i.e. Gorenstein ring. We remark that contains conductor ideal, and bounds for residue. 3-generated semigroups give explicit formulas Thus, in setting can classify those whose at most one (the nearly ones), show eventu...

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...

We construct an algorithmwhich computes the catenary and tame degree of a numerical semigroup. As an example we explicitly calculate the catenary and tame degree of numerical semigroups generated by arithmetical sequences in terms of their first element, the number of elements in the sequence and the difference between two consecutive elements of the sequence.

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

We analyze cohomological properties of the Krichever map and use the results to study Weierstrass cycles in moduli spaces and the tautological ring. Let us consider a point p on a smooth projective connected curve C over C of genus g. We say that a natural number n is a non-gap if there exists a function that is holomorphic on C \p and has a pole of order n at the point p (in other words h0(O(n...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.