Vol. 42, No. 1, 1972

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Structure of right subdirectly irreducible rings. II

M. G. Deshpande

Vol. 42 (1972), No. 1, 39–44

The object of this paper is to determine the structure and properties of right subdirectly irreducible rings which are either local or self-injective. The rings in the latter class form a special case of the so-called right PF rings. By employing the notion of Feller’s X-rings, it is proved that right PF X-rings are finite direct sums of full matrix rings over self-injective right subdirectly irreducible rings. Thus, whether or not right PF X-rings are left PF depends on the answer to the same question for the more elementary case of self-injective right subdirectly irreducible rings.

Mathematical Subject Classification
Primary: 16A48
Secondary: 16A52
Received: 12 January 1971
Revised: 16 June 1971
Published: 1 July 1972
M. G. Deshpande