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A Survey of Rings Generated by Units

Ashish K. Srivastava (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

This article presents a brief survey of the work done on rings generated by their units.

Embedding torsionless modules in projectives.

Carl Faith (1990)

Publicacions Matemàtiques

In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring Rn is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.

Involution Matrix Algebras – Identities and Growth

Rashkova, Tsetska (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 16R50, 16R10.The paper is a survey on involutions (anti-automorphisms of order two) of different kinds. Starting with the first systematic investigations on involutions of central simple algebras due to Albert the author emphasizes on their basic properties, the conditions on their existence and their correspondence with structural characteristics of the algebras. Focusing on matrix algebras a complete description of involutions of the first kind on Mn(F)...

Jordan- and Lie geometries

Wolfgang Bertram (2013)

Archivum Mathematicum

In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...

On some Results Related to Köthe's Conjecture

Agata, Smoktunowicz (2001)

Serdica Mathematical Journal

The Köthe conjecture states that if a ring R has no nonzero nil ideals then R has no nonzero nil one-sided ideals. Although for more than 70 years significant progress has been made, it is still open in general. In this paper we survey some results related to the Köthe conjecture as well as some equivalent problems.

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