On the normal ideals of exchange rings.
On Two-Sided Right Ideals in Chain Domains.
On unit-regular ideals.
On waists of right distributive rings.
One-sided -ideals and -ideals in semirings.
Permutation Identity Near-RIngs and "Localized" Distributivity Conditions.
Polynomial and transformation composition rings.
Polynomial rings over pseudovaluation rings.
Primärkomponentenzerlegung in nichtkommunativen Ringen.
Prime Ideals and Prime Radicals in Near-Rings.
Prime ideals and strongly prime ideals of skew Laurent polynomial rings.
Prime ideals in semirings.
Prime PI-rights in which finitely generated right ideals are principal.
Principal ideals in skew Polynomial rings
Recent progress in special Colombeau algebras: geometry, topology, and algebra
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of modules over the ring of generalized numbers, and algebraic aspects of Colombeau theory. Some open problems are given and directions of further research are outlined.
Reduced near-rings
Regular additively inverse semirings.
Representation of algebraic distributive lattices with ℵ1 compact elements as ideal lattices of regular rings.
We prove the following result: Theorem. Every algebraic distributive lattice D with at most ℵ1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R.(By earlier results of the author, the ℵ1 bound is optimal.) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. Furthermore, if the largest element of D is compact, then one can assume that R is unital, respectively,...
Residual quotient fuzzy subset in near-rings.
Rings Graded By a Generalized Group
The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups. We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. We prove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deduce a characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if R is a Noetherian graded ring, then each summand of it is also a Noetherian module..