Abstract:
We study the length of constructions such as a quotient algebra, a direct sum of algebras, and a subalgebra, which occur in the classical Birkhoff theorem. An upper bound for the length of local algebras is obtained.
Keywords:algebra over a field, finitely generated algebra, length function, Birkhoff theorem, quotient algebra, subalgebra, direct sum of algebras, Jacobson radical.
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