Taming the wild in impartial combinatorial games.
Terms and semiterms
The covariety of perfect numerical semigroups with fixed Frobenius number
Let be a numerical semigroup. We say that is an isolated gap of if A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by the multiplicity of a numerical semigroup . A covariety is a nonempty family of numerical semigroups that fulfills the following conditions: there exists the minimum of the intersection of two elements of is again an element of , and for all such that We prove that the set is a perfect numerical semigroup with...
The factorizable transformation semigroups.
The Frobenius number of geometric sequences.
The intersection graph of a simply ordered semigroup.
The least separative congruence on a weakly commutative semigroup
The local catenativity of DOL-sequences in free commutative monoids is decidable in the binary case
The number of commutative semigroups of order N.
The rank of a commutative semigroup
The concept of rank of a commutative cancellative semigroup is extended to all commutative semigroups by defining as the supremum of cardinalities of finite independent subsets of . Representing such a semigroup as a semilattice of (archimedean) components , we prove that is the supremum of ranks of various . Representing a commutative separative semigroup as a semilattice of its (cancellative) archimedean components, the main result of the paper provides several characterizations...
The semigroup of nonempty finite subsets of integers.
The semigroup of nonempty finite subsets of rationals.
The structure of commutative ideal semigroups.
The tame degree and related invariants of non-unique factorizations
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.
The theory of characters of commutative Hausdorff bicompact semigroups
The translational degree of a semigroup.
Tolerance distributive and tolerance modular varieties of commutative semigroups
Trees in commtative nil-semigroups of index two