On maximal chains in the lattice of module topologies.
On modules in which idempotent reducts form a chain
On near-ring ideals with -derivation
Let be a -prime left near-ring with multiplicative center , a -derivation on is defined to be an additive endomorphism satisfying the product rule for all , where and are automorphisms of . A nonempty subset of will be called a semigroup right ideal (resp. semigroup left ideal) if (resp. ) and if is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let be a
On nearrings with derivation.
On ordered division rings
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel's axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under x ↦ xa² for non-zero a, in place of requiring that positive elements have a positive product. Our aim in this work is to study this type of ordering in the case of a division ring. We show that it actually behaves just as in the commutative...
On ordered division rings
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel’s axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under for nonzero , instead of requiring that positive elements have a positive product. In this work, this type of ordering is studied in the case of a division ring. It is shown that it actually behaves the same as in the commutative...
On prime and semiprime near-rings with derivations.
On prime near-rings with generalized derivation.
On regular elements in an incline.
On regular endomorphism rings of topological Abelian groups
We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups for which is regular is given.
On regular semigroup rings.
On right ideals and derivations in prime rings with Engel condition
On rings whose centers are Galois extensions
On -Noetherian rings
Let be a commutative ring and a given multiplicative set. Let be a strictly ordered monoid satisfying the condition that for every . Then it is shown, under some additional conditions, that the generalized power series ring is -Noetherian if and only if is -Noetherian and is finitely generated.
On semigroup graded PI-algebras.
On separable Abelian extensions of rings.
On Separable Subalgebras of Azumaya Algebras
On skew derivations as homomorphisms or anti-homomorphisms
Let be a prime ring with center and be a nonzero ideal of . In this manuscript, we investigate the action of skew derivation of which acts as a homomorphism or an anti-homomorphism on . Moreover, we provide an example for semiprime case.
On small injective, simple-injective and quasi-Frobenius rings.
On some additive mappings in rings with involution.