Simplen-associative rings

Homotopy Theory of Associative Rings

A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a quasi-isomorphism (or weak equivalence) for rings and shows that similar to spaces the derived category obtained by inverting the quasiisomorphisms is natura...

Foxby Equivalence over Associative Rings

We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C. We then study the classes of C-flats, C-projectives, and C-injectives, and use them to provide a characterization of the modules in the Auslander and Bass classes. We extend Foxby equivalence to this new setting. This...

Commutativity of Associative Rings through Astreb

Let m 0; r 0; s 0; q 0 be xed integers. Suppose that R is an associative ring with unity 1 in which for each x; y 2 R there exist polynomials f(X) 2 X 2 Z ZX]; g(X); h(X) 2 XZ ZX] such that f1?g(yx m)gx; x r y ? x s f(yx m)x q ]f1?h(yx m)g = 0. Then R is commu-tative. Further, result is extended to the case when the integral exponents in the above property depend on the choice of x and y. Final...

A Kadison–Dubois representation for associative rings

In this paper we give a general theorem that describes necessary and sufficient conditions for a module to satisfy the so–called Kadison–Dubois property. This is used to generalize Jacobi’s version of the Kadison–Dubois representation to associative rings. We apply this representation to obtain a noncommutative algebraic and geometric version of Putinar’s Positivstellensatz. We finish the paper...

Power-associative Rings of Characteristic Two