In this paper, we make use of generalized derivations to scrutinize the deportment prime ideal satisfying certain algebraic $*$-identities in rings with involution. specific cases, structure quotient ring $\mathscr{R}/\mathscr{P}$ will be resolved, where $\mathscr{R}$ is an arbitrary and $\mathscr{P}$ a also find behaviour associated involving ideals. Finally, conclude our paper applications pr...

Let H ⊆ P5 denote the hypersurface of binary quintics in involution, with defining equation given by the Hermite invariant H. In §2 we find the singular locus of H, and show that it is a complete intersection of a linear covariant of quintics. In §3 we show that the projective dual of H can be canonically identified with itself via an involution. The Jacobian ideal of H is shown to be perfect o...

A well-known result of Posner’s second theorem states that if the commutator each element in a prime ring and its image under nonzero derivation are central, then is commutative. In present paper, we extended this bluestocking to an arbitrary with involution involving ideals. Further, apart from proving several other interesting exciting results, established ∗-version Vukman’s theorem. Precisel...

‎Let $R$ be a ring with involution $*$‎. ‎An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

Let R be a ring with involution. An additive mapping T : R → R is called a left ∗-centralizer (resp. Jordan left ∗-centralizer) if T (xy) = T (x)y∗ (resp. T (x2) = T (x)x∗) holds for all x, y ∈ R, and a reverse left ∗-centralizer if T (xy) = T (y)x∗ holds for all x, y ∈ R. The purpose of this paper is to solve some functional equations involving Jordan left ∗-centralizers on some appropriate su...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Lactation mastitis is a common, but poorly understood, inflammatory breast disease that is a significant health burden. A better understanding of the aetiology of mastitis is urgently required, and will assist in the development of improved prevention and treatment strategies in both human and animal species. Studies in mice have the potential to greatly assist in identifying new drug candidate...

in this paper, we associate canonically a precyclic mod- ule to a regular multiplier hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closely related to the “minus part” of the class group. We present a deterministic polynomial-time algorithm for the following problem, which may be viewed as a special case of the principal ideal testing problem: given a C...

‎let $r$ be a ring with involution $*$‎. ‎an additive mapping $t:rto r$ is called a left(respectively right) centralizer if $t(xy)=t(x)y$ (respectively $t(xy)=xt(y)$) for all $x,yin r$‎. ‎the purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.