We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

Library research dengan pendekatan deduksi-induksi ini bertujuan untuk mengkaji kesemiprimaan mendasar aljabar tak bebas yang dibangun secara hingga atas ring komutatif unital. Tujuan praktis penelitian adalah mengaplikasikan suatu contoh semiprima non-komutatif pada protokol autentikasi berdasarkan masalah dekomposisi. Di samping itu, lebih umum dari semiprima, hal ditunjukkan penyangkal. Hasi...

Miriam Cohen raised the question whether the smash product of a semisimple Hopf algebra and a semiprime module algebra is semiprime. In this paper we show that the smash product of a commutative semiprime module algebra over a semisimple cosemisimple Hopf algebra is semiprime. In particular we show that the central H-invariant elements of the Martindale ring of quotients of a module algebra for...

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S. Keywords—Semigroup, Regular(intra-regular) semigroup, In...

Jacobson introduced the concept of K-rings, continuing the investigation of Kaplansky and Herstein into the commutativity of rings. In this note we focus on the ring-theoretic properties of K-rings. We first construct basic examples of K-rings to be handled easily. It is shown that a semiprime K-ring of bounded index of nilpotency is a commutative domain. It is proved that if R is a prime K-rin...

This paper is focused on the commutativity of laws semiprime rings, which satisfy some algebraic identities involving homoderivations ideals. It provides new and notable results that will interest researchers in this field, such as “R contains a nonzero central ideal if R admits homoderivation δ I δ(I)⊆Z where ring with center Z R”. Moreover, research also generalizes previously published liter...

We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propo...