Local tameness and the finiteness of the catenary degree are two crucial finiteness conditions in the theory of non-unique factorizations in monoids and integral domains. In this note, we refine the notion of local tameness and relate the resulting invariants with the usual tame degree and the -invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties.
We enlarge the problem of valuations of triads on so called lines. A line in an -structure (it means that is a semigroup and is an automorphism or an antiautomorphism on such that ) is, generally, a sequence , , (where is the class of finite integers) of substructures of such that holds for each . We denote this line as and we say that a mapping is a valuation of the line in a line if it is, for each , a valuation of the triad in . Some theorems on an existence of...
2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14.Let H be a 4-semigroup, i.e., a numerical semigroup whose minimum positive element is four. We denote by 4r(H) + 2 the minimum element of H which is congruent to 2 modulo 4. If the genus g of H is larger than 3r(H) − 1, then there is a cyclic covering π : C −→ P^1 of curves with degree 4 and its ramification point P such that the Weierstrass semigroup H(P) of P is H (Komeda [1]). In this paper it is showed that...
We show that in a cyclic group with elements every zero-sumfree sequence with length contains some element of order with high multiplicity.