Ideal theory in commutative semigroups.
Ideal-theoretic characterizations of valuation and Prüfer monoids
It is well known that an integral domain is a valuation domain if and only if it possesses only one finitary ideal system (Lorenzen -system of finite character). We prove an analogous result for root-closed (cancellative) monoids and apply it to give several new characterizations of Prüfer (multiplication) monoids and integral domains.
Idempotent semigroups and tropical algebraic sets
The tropical semifield, i.e., the real numbers enhanced by the operations of addition and maximum, serves as a base of tropical mathematics. Addition is an abelian group operation, whereas the maximum defines an idempotent semigroup structure. We address the question of the geometry of idempotent semigroups, in particular, tropical algebraic sets carrying the structure of a commutative idempotent semigroup. We show that commutative idempotent semigroups are contractible, that systems of tropical...
Implicative commutative semigroups are equivalent to a class of BCK algebras.
In memory of Jaroslav Ježek
Interpolation properties and tensor product of semigroups.
Interpolation property in semigroups.
Irreducibility of ideals in a one-dimensional analytically irreducible ring
Let be a one-dimensional analytically irreducible ring and let be an integral ideal of . We study the relation between the irreducibility of the ideal in and the irreducibility of the corresponding semigroup ideal . It turns out that if is irreducible, then is irreducible, but the converse does not hold in general. We collect some known results taken from [5], [4], [3] to obtain this result, which is new. We finally give an algorithm to compute the components of an irredundant decomposition...
Isomorphisms of products