Vol. 89, No. 1, 1980

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Maps on simple algebras preserving zero products. I. The associative case

Warren James Wong

Vol. 89 (1980), No. 1, 229–247
Abstract

Recent studies of linear transformations of various types on the space of n × n matrices over a field suggest the general problem of finding the semilinear transformations f on an algebra A over a field k, with the property that

xy = 0 ⇒ f(x)f(y) = 0,

where x,y A. In this article such maps are determined for a class of primitive associative algebras, including the case of bijective maps f on a finite-dimensional simple associative algebra A.

Mathematical Subject Classification 2000
Primary: 15A04
Secondary: 16A20
Milestones
Received: 31 May 1978
Published: 1 July 1980
Authors
Warren James Wong