In this paper we brieƒy discuss Rings — an ecient lightweight library for univariate and multivariate polynomial arithmetic over arbitrary coecient rings. Basic algebra, GCDs and factorization of polynomials are implemented with the use of modern asymptotically fast algorithms. Rings provides a clean API for algebra and a fully typed hierarchy of mathematical structures. Scala API additionall...

In this paper we survey some results on the structure of noncommutative rings. We focus particularly on nil rings, Jacobson radical rings and rings with finite Gelfand–Kirillov dimension. Mathematics Subject Classification (2000). 16-02, 16-06, 16N40, 16N20, 16N60, 16D60, 16P90.

A ring [Formula: see text] is said to be clean if each element of can written as the sum a unit and an idempotent. weakly either or difference idempotent, feebly every text], where are orthogonal idempotents. Clearly, rings both them clean. In recent paper (J. Algebra Appl. 17 (2018) 1850111 (5 pp.)), McGoven characterized when group clean, distinct primes. this paper, we consider more general ...