Commutative semigroups with almost transitive endomorphism semirings
Commutative semigroups with few fully invariant congruences I.
Commutative semigroups with few fully invariant congruences II.
Commutative semigroups with self-dual lattice of subsemigroups.
Commutative zeropotent semigroups
Commutative zeropotent semigroups with few invariant congruences
Commutative semigroups satisfying the equation and having only two -invariant congruences for an automorphism group are considered. Some classes of these semigroups are characterized and some other examples are constructed.
Commutative zeropotent semigroups with few prime ideals
We construct an infinite commutative zeropotent semigroup with only two prime ideals.
Computing finite commutative semigroups.
Computing the integral closure of an affine semigroup.
Congruence monoids
Corrigendum: On linear algebraic semigroups. III.
Countable Hausdorff spaces with countable weight
Demi-groupes commutatifs réticulés résidués intégralement clos
Differences in sets of lengths of Krull monoids with finite class group
Let be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary -groups have the same system of sets of lengths if and only if they are isomorphic.
Direct decomposability of tolerances and congruences on semigroups
Diversity in inside factorial monoids
In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant complementary...
Diversity in monoids
Let be a (commutative cancellative) monoid. A nonunit element is called almost primary if for all , implies that there exists such that or . We introduce a new monoid invariant, diversity, which generalizes this almost primary property. This invariant is developed and contextualized with other monoid invariants. It naturally leads to two additional properties (homogeneity and strong homogeneity) that measure how far an almost primary element is from being primary. Finally, as an application...
Eine Bemerkung zur eindeutigen Primfaktorenzerlegung in Halbgruppen.
Elasticity in certain block monoids via the Euclidean table
Embedding in globals of finite semilattices