In the present paper we develop a small cancellation theory for associative algebras with basis of invertible elements. Namely, study quotients group algebra free and introduce three axioms corresponding defining relations. We show that obtained ring is non-trivial. Moreover, this enjoys global filtration agrees relations, find as vector space establish structure theorems. also provide revision...

Let R be a unital *-ring and let a, b,w ? R. In this paper, we give some new characterizations on w-core inverses in particular, it is shown that invertible if only w(aw)n?1- core for any positive integer n, which case, the representations of inverse w(aw)n?1-core are both presented. We further characterize by Hermitian elements (or projections) units.

Several applications in communication, control, and learning require approximating target distributions to within small informational divergence. The additional requirement of invertibility usually leads using encoders that are one-to-one mappings, also known as distribution matchers. However, even the best have divergences grow logarithmically with block length. To overcome this limitation, an...