Three Papers on Algebras and Their Representations

Abstract

Part I. Free associative algebras and inverting homomorphisms of rings: Introduction Free algebras and algebras with a single relation Inverting homomorphisms of rings Part II. Representations of algebras by triangular matrices: Conventions and notation Introduction Representability of triangular categories and graded algebras Representation of algebras by triangular matrices. Algebras with diagonal Special representations of nilpotent graded algebras References Part III. Embedding rings in radical rings and rational identities of radical algebras: Introduction Index of notation Absence of a finite basis of quasi-identities for the quasi-variety of rings embeddable in radical rings Examples of noninvertible rings embeddable in groups Representation of finite-dimensional Lie algebras in radical rings Rational identities of radical algebras References.