The Tensor Product of Semilocal Algebras
العليان, احمد الغامدي وحنان . 2014
M. Sweedler [5] proved that if a tensor product of two commutative
algebras over a field is local then each of the algebras is local and that the
tensor product of the residue field is local. Moreover, one of the algebras
most be algebraic over the ground field. But the tensor product of two
Artinian algebras over a field in general need not be Artinian. In this
paper we generalize M. Sweedler theorem and shows that tensor product
of two algebras over a field K is semilocal if and only if each of these
algebras is semilocal.
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Abstract
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