We prove a new characterization of graded von Neumann regular rings involving the recently introduced class nearly epsilon-strongly rings. As our main application, we generalize Hazrat's result that Leavitt path algebras over fields are regular. More precisely, show algebra LR(E) with coefficients in unital ring R is if and only also both corner skew Laurent polynomial semiprimitive semiprime. ...

The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. D-radicals of ideals are introduced and investigated. In particular, the prime radi...

Let R be a ring with center Z and I a nonzero ideal of R. An additive mapping F : R → R is called a generalized derivation of R if there exists a derivation d : R → R such that F xy F x y xd y for all x, y ∈ R. In the present paper, we prove that if F x, y ± x, y for all x, y ∈ I or F x ◦ y ± x ◦ y for all x, y ∈ I, then the semiprime ring R must contains a nonzero central ideal, provided d I /...

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...

Let A⊆B be a ring extension and G set of A-submodules B. We introduce class closure operations on (which we call multiplicative (A,B,G)) that generalizes the classes star, semistar semiprime operations. study how Mult(A,B,G) these varies when A, B or vary, behaves under homomorphisms. As an application, show to reduce star analytically unramified one-dimensional Noetherian domains closures fini...

In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.

The notions of prime(semiprime) fuzzy h-ideal(h-biideal, h-quasi-ideal) in Γ-hemiring are introduced and some of their characterizations are obtained by using ”belongingness(∈)” and ”quasi − coincidence(q)”. Cartesian product of prime(semiprime) fuzzy h-ideals of Γ-hemirings are also investigated. Keywords—Γ-hemiring, Fuzzy h-ideals, Prime fuzzy left h-ideal, Prime(semiprime) (∈,∈ ∨q)-fuzzy lef...

Group automata occur in the Krohn-Rhodes Decomposition Theorem and have been extensively investigated in the literature. The incidence rings of group automata were introduced by the first author in analogy with group rings and incidence rings of graphs. The main theorem of the present paper gives a complete description of the structure of incidence rings of group automata in terms of matrix rin...

Albert is an interactive computer system for building nonassociative algebras [2]. In this paper, we suggest certain techniques for using Albert that allow one to posit and test hypotheses e ectively. This process provides a fast way to achieve new results, and interacts nicely with traditional methods. We demonstrate the methodology by proving that any semiprime ring, having characteristic 6= ...

Let R be a ring and let I 6= R be an ideal of R. Then I is said to be a completely prime ideal of R if R/I is a domain and is said to be completely semiprime if R/I is a reduced ring. In this paper, we introduce a new class of rings known as completely prime ideal rings. We say that a ring R is a completely prime ideal ring (CPI-ring) if every prime ideal of R is completely prime. We say that a...