Free Group Algebras in Division Rings with Valuation II

Triangulaizability of Algebras Over Division Rings

triangulaizability of algebras over division rings

Pseudo-Valuation ‏‎Near ‎ring‎ and Pseudo-Valuation N-group in Near Rings

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

Some Results Relevant to Embeddability of Rings (especially Group Algebras) in Division Rings

P. M. Cohn showed in 1971 that given a ring R, to describe, up to isomorphism, a division ring D generated by a homomorphic image of R is equivalent to specifying the set of square matrices over R which map to singular matrices over D, and he determined the conditions that such a set of matrices must satisfy. The present author later developed another version of this data, in terms of closure o...

Pseudo-almost valuation rings

The aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎It is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...