The Tensor Product of Semilocal Algebras

مقال فى مجلة
العليان,  احمد الغامدي وحنان . 2014
نوع عمل المنشور
ورقة علمية
اسم الناشر
HIKARI
مجلة/صحيفة
International Journal of Algebra
تاريخ المؤتمر
ملخص المنشورات

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.