The anti-homomorphic image of fuzzy ideals, fuzzy ideals of near-rings and anti ideals are discussed in this note. A necessary and sufficient condition has been established for near-ring anti ideal to be characteristic. Keywords—Fuzzy Ideals, Anti fuzzy subgroup, Anti fuzzy ideals, Anti homomorphism, Lower α level cut.

The following result is proved: Let R be a 2-torsion free semiprime ring, and let T : R → R be an additive mapping, related to a surjective homomorphism θ : R → R, such that 2T (x2) = T (x)θ(x) + θ(x)T (x) for all x ∈ R. Then T is both a left and a right θ-centralizer.

We establish a formula for the classes of certain tori in the Grothendieck ring of varieties, expressing them in terms of the natural lambda-structure on the Grothendieck ring. More explicitly, we will see that if L∗ is the torus of invertible elements in the n-dimensional separable k-algebra L, then the class of L∗ can be expressed as an alternating sum of the images of the spectrum of L under...

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

We define the Homomorphism Extension (HomExt) problem: given a group G, a subgroup M ≤ G and a homomorphism φ : M → H , decide whether or not there exists a homomorphism φ̃ : G → H extending φ, i.e., φ̃|M = φ. This problem arose in the context of list-decoding homomorphism codes but is also of independent interest, both as a problem in computational group theory and as a new and natural problem i...

A brief comment about items (3) and (4). If H is a subgroup of G the inclusion map is an injective homomorphism from H to G . On the other hand, the image of an injective homomorphism α : H −→ G is a subgroup that is isomorphic to H . So the study of injective homomorphisms is (up to isomorphism) the study of subgroups. After studying subgroups, we defined normal subgroup and showed several equ...

Let G be a finite group and R a strongly G-graded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory answer given by Aljadeff and Robinson [3]. Another partial answer for skew group rings was given by Al...

Symmetry-related problems can be addressed by means of group theory, and ring theory seen as an extension additive theory. Ring a significant topic in abstract algebra, is currently active diverse range study domains across the disciplines mathematics, theoretical physics coding The ideals vital to rings wide ways. uncertainties present information are well q-rung orthopair fuzzy set (q-ROFS). ...

the effect of alkyl substituents on the c-phenyl and/or the n-phenyl ring of benzophenylhydroxamic acid on their molecular structure and hydrogen bonding has been investigated. the predominant configuration in chcl3 is determined by steric and electronic effects. substituents on the c-phenyl ring favor the cis configuration, while substituents in the n-phenyl ring favor a trans configuration. t...