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On Maximally Central Algebras
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Let A be a primary algebra with unit element over a field K and Z its center. Let Ā be the simple residue class algebra of A modulo its radical. Then it is known, and can readily be seen, that there holds the inequality where t is the rank of A over its center. We call A maximally central if in particular i.e. if the rank [Z: K] takes its maximum value. Further, an algebra which is a direct sum of those primary algebras will be called maximally central too. The notion was introduced in Azumaya-Nakayama [5], as a by-product of the study of absolutely uni-serial algebras.
Title: On Maximally Central Algebras
Description:
Let A be a primary algebra with unit element over a field K and Z its center.
Let Ā be the simple residue class algebra of A modulo its radical.
Then it is known, and can readily be seen, that there holds the inequality where t is the rank of A over its center.
We call A maximally central if in particular i.
e.
if the rank [Z: K] takes its maximum value.
Further, an algebra which is a direct sum of those primary algebras will be called maximally central too.
The notion was introduced in Azumaya-Nakayama [5], as a by-product of the study of absolutely uni-serial algebras.
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