By Gelfand-Neumark duality, the category C∗Alg of commutative C∗algebras is dually equivalent to the category of compact Hausdorff spaces, which by Stone duality, is also dually equivalent to the category uba` of uniformly complete bounded Archimedean `-algebras. Consequently, C∗Alg is equivalent to uba`, and this equivalence can be described through complexification. In this article we study u...

Suppose that a finite group G admits a Frobenius group of automorphisms FH with kernel F and complement H such that the fixed-point subgroup of F is trivial: CG(F ) = 1. In this situation various properties of G are shown to be close to the corresponding properties of CG(H). By using Clifford’s theorem it is proved that the order |G| is bounded in terms of |H| and |CG(H)|, the rank of G is boun...

Abstract A local ring R is regular if and only every finitely generated -module has finite projective dimension. Moreover, the residue field k a test module: This characterization can be extended to bounded derived category $\mathsf {D}^{\mathsf f}(R)$ , which contains small objects regular. Recent results of Pollitz, completing work initiated by Dwyer–Greenlees–Iyengar, yield an analogous for ...

The Parameterized Model Checking Problem (PMCP) is to decide whether a temporal property holds for a uniform family of systems, , comprised of finite, but arbitrarily many, copies of a template process . Unfortunately, it is undecidable in general [3]. In this paper, we consider the PMCP for systems comprised of processes arranged in a ring that communicate by passing messages via tokens whose ...

The Lifting Idempotent Property (LIP) of ideals in commutative rings inspired the study Boolean lifting properties context other concrete algebraic structures (MV-algebras, l-groups, BL-algebras, bounded distributive lattices, residuated etc.), as well for some types universal algebras (C. Muresan and author defined studied Congruence (CBLP) congruence modular algebras). A ideal a ring R is an ...

let $r$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$ and $f(x)=a_0+a_1x+cdots+a_nx^n$ be a nonzero skew polynomial in $r[x;alpha]$. it is proved that if there exists a nonzero skew polynomial $g(x)=b_0+b_1x+cdots+b_mx^m$ in $r[x;alpha]$ such that $g(x)f(x)=c$ is a constant in $r$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $r$ such tha...

we observe some new characterizations of $n$-presented modules. using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...