Results 41 to 50 of about 104 (51)

Fully Coprime Comodules and Fully Coprime Corings [PDF]

Applied Categorical Structures (Special Issue 2006), 2006
Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules).
arxiv  

Skew $N$-Derivations on Semiprime Rings [PDF]

arXiv, 2012
For a ring $R$ with an automorphism $\sigma$, an $n$-additive mapping $\Delta:R\times R\times... \times R \rightarrow R$ is called a skew $n$-derivation with respect to $\sigma$ if it is always a $\sigma$-derivation of $R$ for each argument. Namely, it is always a $\sigma$-derivation of $R$ for the argument being left once $n-1$ arguments are fixed by $
arxiv  

Prime ideals of skew PBW extensions [PDF]

arXiv, 2014
In this paper we describe the prime ideals of some important classes of skew PBW extensions, using the classical technique of extending and contracting ideals. Skew PBW extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras,
arxiv  

Extended modules and Ore extensions [PDF]

arXiv, 2015
In this paper we investigate extended modules for a special class of Ore extensions. We will assume that $R$ is a ring and $A$ will denote the Ore extension $A:=R[x_1,\dots,x_n;\sigma]$ for which $\sigma$ is an automorphism of $R$, $x_ix_j=x_jx_i$ and $x_ir=\sigma(r)x_i$, for every $1\leq i,j\leq n$.
arxiv  

A relationship between 2-primal modules and modules that satisfy the radical formula [PDF]

International Electronic Journal of Algebra, 18 (2015) 34-45, 2017
The coincidence of the set of all nilpotent elements of a ring with its prime radical has a module analogue which occurs when the zero submodule satisfies the radical formula. A ring $R$ is 2-primal if the set of all nilpotent elements of $R$ coincides with its prime radical.
arxiv  

Are zero-symmetric simple nearrings with identity equiprime? [PDF]

arXiv
We show that there exist zero-symmetric simple nearrings with identity which are not equiprime, solving a longstanding open problem.
arxiv  

Structure of a factor ring $R/P$ in terms of differential identities involving a new kind of involution [PDF]

arXiv
Let $R$ be a ring and $P$ a prime ideal of $R.$ In this paper, we establish some commutativity criteria for the factor ring $R/P$ in terms of derivations of $R$ satisfying some algebraic identities involving a new kind of involution in relation with $P.$
arxiv  

A constructive counterpart of the subdirect representation theorem for reduced rings [PDF]

arXiv
We give a constructive counterpart of the theorem of Andrunakievi\v{c} and Rjabuhin, which states that every reduced ring is a subdirect product of domains. As an application, we extract a constructive proof of the fact that every ring $A$ satisfying $\forall x\in A. x^3=x$ is commutative from a classical proof.
arxiv  

Effects of endomorphisms on the commutativity of banach algebras [PDF]

arXiv
In this article, we are interested in endomorphism's impact on the commutativity of a Banach algebra. Our research uses a topological approach, drawing on specific results from functional analysis and algebraic techniques.\;Also, we provide examples to show that we need certain assumptions.
arxiv  

The properties of Banach algebras affected by differential identities [PDF]

arXiv
Let $B$ be a Banach algebra. The interest of this article lies in the study of the commutativity of B if certain specific algebraic identities hold over a non-empty open subset of B. The limitations imposed in the hypothesis of our results are justified by some examples.
arxiv