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Weakly semi-simple finite-dimensional algebras

1966
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Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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Let A be a finite-dimensional (associative) algebra over an arbitrary field F. We shall say that a semi-group 5 is a translate of A if there exist an algebra B over F and an epimorphism : B -» F such that A = 0<£ _1 and S = 1<£ -1 . It is shown in (2) that any such semi-group 5 has a kernel (defined below) that is completely simple in the sense of Rees. Following Stefan Schwarz (4), we define the radical R(S) of S to be the union of all ideals I oi S such that some power I n of / lies in the

doi:10.4153/cjm-1966-046-7
fatcat:minu6vmbb5br7k7aervv2qgscu