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= ...

In this paper, we employed bipolar fuzzy set theory to hemi-rings and we popularized notation of bipolar valued fuzzy interior h-ideal, bipolar-valued fuzzy prime h-ideal, bipolar-valued fuzzy semiprime h-ideal, bipolar-valued fuzzy h-bi-ideal and bipolarvalued fuzzy h-quasi-ideal. We also introduced some basic properties and definition of bipolar-valued fuzzy h-ideals of hemi-ring. Then we int...

Let R be a semiprime ring and let F, f : R → R be (not necessarily additive) maps satisfying F (xy) = F (x)y + xf(y) for all x, y ∈ R. Suppose that there are integers m and n such that F (uv) = mF (u)F (v) + nF (v)F (u) for all u, v in some nonzero ideal I of R. Under some mild assumptions on R, we prove that there exists c ∈ C(I) such that c = (m + n)c2, nc[I, I] = 0 and F (x) = cx for all x ∈...

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...

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.

In this paper, we initiate the study of prime bi-ideals (fuzzy bi-ideals) in semirings. We define strongly prime, prime, semiprime, irreducible and strongly irreducible bi-ideals in semirings. We also define strongly prime, semiprime, irreducible, strongly irreducible fuzzy bi-ideals of semirings. We characterize those semirings in which each bi-ideal (fuzzy bi-ideal) is prime (strongly prime).

In this paper, properties of ideal I semiprime ring R with multiplicative generalized (α,β)- reverse derivation determined not necessarily additive map d is studied. We previous studies for different derivations to F. show that [β(p),d(p)]I=0 all p∈I or [d(p)],α(p)]I=0 under the given conditions. Also, we give relationship between and anti-automorphism α automorphism β R. Under conditions, exam...

the aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered ag-groupoids with left identity. these concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered ag-groupoids, so it seems to be interesting to study them.

out, R will represent an associative ring with center Z(R). As usual the commutator xy−yx will be denoted by [x,y]. We will use basic commutator identities [xy,z] = [x,z]y+x[y,z] and [x,yz]= [x,y]z+y[x,z]. Recall that a ring R is prime if aRb = (0) implies that a = 0 or b = 0, and is semiprime if aRa = (0) implies a = 0. An additive mapping x x∗ on a ring R is called involution in case (xy)∗ = ...

Let I be a non-zero left ideal of r-ring M satisfying the condition alpha b beta c= c for all a,b,c, e and alpha, r. We show that contains non-trivial central if is semiprime which admits an appropriate derivations on I, also commutative prime admitting centralizing derivation I. next give some characterizations when generalized act as homomorphisms anti-homomorphisms or two-sided ideals gamma ...