Vol. 44, No. 2, 1973

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Semi-primary split rings

Garry Arthur Helzer

Vol. 44 (1973), No. 2, 541–552

This paper is concerned with Hochschild’s “maximal algebra” which has also been discussed by Jans, Jans and Nakayama, and Zaks.

A category of rings for which the maximal algebra construction is valid is first defined. These are the “split rings” of the title. These rings include the split rings introduced by Jans and Nakayama but they need not be semi-primary. A second category consisting of a kind of sheaf over a directed graph is introduced. Using this second category the maximal algebra construction is exhibited as a composition of adjoint functors, and hence gives the universal mapping property of the maximal algebra. The properties of the sheaf category are then used to show that a semi-primary split ring is the image of a semi-primary ring of a special type.

Mathematical Subject Classification 2000
Primary: 18G99
Secondary: 16A62
Received: 11 June 1971
Revised: 6 September 1972
Published: 1 February 1973
Garry Arthur Helzer