On a Class with Rings with Inverse Weak Algorithm.
On a problem of Bertram Yood
In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.
On -radicals
On abelian separable extensions and Galois sets of rings
On clean ideals.
On essential left ideals of associative rings.
On -ideals of semirings.
On -fuzzy ideals in semirings. I
In this paper we extend the concept of an -fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring , and we show that each level left (resp. right) ideal of an -fuzzy left (resp. right) ideal of is characteristic iff is -fuzzy characteristic.
On -fuzzy ideals in semirings. II
We study some properties of -fuzzy left (right) ideals of a semiring related to level left (right) ideals.
On matrix near-rings.
On pairs of subrings with a common set of proper ideals.
On presentations of semigroup rings
Siano un ideale di un anello e una congruenza su un semigruppo . Consideriamo l'anello semigruppo come un'immagine omomorfa dell'anello semigruppo . Questo è fatto in tre passi: prima studiando l'anello semigruppo , poi e infine combinando i due casi speciali. In ciascun caso, determiniamo l'ideale che è il nucleo dell'omomorfismo in questione. I risultati corrispondenti per le -algebre, dove è un anello commutativo, possono essere facilmente dedotti. Alcuni raffinamenti, casi speciali...
On properties of fuzzy left -ideals in hemirings with -norms.
On quasi-ideals and bi-ideals in ternary semirings.
On quasi-ideals of semirings.
On rings with a unique proper essential right ideal
Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and is Artin semisimple...
On strongly 0-prime ideals in near-rings.
On strongly prime semiring.
On -fuzzy ideals in nearrings.
On the Idealizer of a Subring.