Ideal extensions of irreductive semigroups.
Ideal nil-extensions of semigroups with semimodular congruence lattices.
Ideal systems of intersection and product type
Ideal theory in commutative semigroups.
Ideals and Green's relations in ordered semigroups.
Ideals are greater on the left.
Ideals in selfdistributive groupoids
Products of (left) ideals in selfdistributive groupoids are studied.
Ideals in transformation semigroups
Ideals of Schur-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 Boolean matrices.
Idempotent Bounded Semi-Groups.
Idempotent cross-sections of J-classes.
Idempotent Endomorphisms on Standard Threads.
Idempotent pre-generalized hypersubstitutions of type .
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...
Idempotent semigroups generated by threads, I.
Idempotent semigroups generated by threads II.
Idempotent separating congruences on an orthodox semigroup via the least inverse congruence.
Idempotent-determined congruences on inverse semigroups.