Abstract In this paper we develop a number of results and notions concerning Positivstellensätze for semirings (preprimes) commutative unital real algebras. First reduce the Archimedean Positivstellensatz to corresponding result quadratic modules. Various applications are investigated. A general with denominators is proved filtered algebras semirings. As an application derive denominator-free c...

A pro-C∗-algebra is a (projective) limit of C∗-algebras in the category of topological ∗algebras. From the perspective of non-commutative geometry, pro-C∗-algebras can be seen as non-commutative k-spaces. An element of a pro-C∗-algebra is bounded if there is a uniform bound for the norm of its images under any continuous ∗-homomorphism into a C∗-algebra. The ∗-subalgebra consisting of the bound...

For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earl...

We give a short answer to the question in the title: dendrits. Precisely we show that the C∗-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category C of all (not necessarily commutative) unital C∗-algebras if and only if X is an absolute retract of dimension dimX ≤ 1 or, equivalently, that X is a dendrit.

In [9], Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras. We make some remarks on the topological stable rank of commutative, unital Banach algebras. In particular, we prove that tsr(A) ≥ t...

We extend the notions of irreducibility and periodicity of a stochastic matrix to a unital positive linear map © on a finite-dimensional C∗algebra A and discuss the non-commutative version of the Perron-Frobenius theorem. For a completely positive linear map © with ©(a) = ∑ l Ll ∗aLl, we give conditions on the Ll’s equivalent to irreducibility or periodicity of ©. As an example, positive linear...

By recent results of M. Stronkowski, it is known that not all modes embed as subreducts into semimodules over commutative unital semirings. Related to this problem is the problem of constructing a (commutative unital) semiring defining the variety of semimodules whose idempotent subreducts lie in a given variety of modes. We provide a general construction of such semirings, along with basic exa...

Library research dengan pendekatan deduksi-induksi ini bertujuan untuk mengkaji kesemiprimaan mendasar aljabar tak bebas yang dibangun secara hingga atas ring komutatif unital. Tujuan praktis penelitian adalah mengaplikasikan suatu contoh semiprima non-komutatif pada protokol autentikasi berdasarkan masalah dekomposisi. Di samping itu, lebih umum dari semiprima, hal ditunjukkan penyangkal. Hasi...

Comtrans algebras are unital modules over a commutative ring R, equipped with two basic trilinear operations: a commutator [x, y, z] satisfying the left alternative identity [x, x, y] = 0, (1.1) and a translator 〈x, y, z〉 satisfying the Jacobi identity 〈x, y, z〉+ 〈y, z, x〉+ 〈z, x, y〉 = 0, (1.2) such that together the commutator and translator satisfy the comtrans identity [x, y, x] = 〈x, y, x〉....

We introduce notions of dimension and dynamical entropy for unital C∗algebras “metrized” by means of cLip-norms, which are complex-scalar versions of the Lip-norms constitutive of Rieffel’s compact quantum metric spaces. Our examples involve the UHF algebras Mp∞ and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical c...