Radicals of supplementary semilattice sums of associative rings

on direct sums of baer modules

the notion of baer modules was defined recently

Subdirect Sums of Rings

Artinian Band Sums of Rings

Band sums of associative rings were introduced by Weissglass in 1973. The main theorem claims that the support of every Artinian band sum of rings is finite. This result is analogous to the well-known theorem on Artinian semigroup rings. 1991 Mathematics subject classification (Amer. Math. Soc): primary 16P20, 16W50; secondary 20M25. Let B be a band, that is, a semigroup consisting of idempoten...

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...

Computing Sums of Radicals in Polynomial Time

For sums of radicals P k i=1 i d i p i, where i; i are elements of some real algebraic number eld Q(); d i p i 2 R; we present a deterministic polynomial time algorithm to decide whether the sum is zero. The time is polynomial in the number of bits required to represent , the i's, i's and di's. The algorithm can be extended to sums of complex radicals over certain complex algebraic number elds.