THE TRACE AS AN ALGEBRA HOMOMORPHISM
THE TRACE AS AN ALGEBRA HOMOMORPHISM
Let V be an (appropriately restricted) module over a commutative ring R with unit. Then, denoting by \(\Lambda^ pV\) the p-th exterior power of V and considering the direct sum \(\coprod_ pEnd \Lambda^ pV\), a product on this space is defined, such that with a suitable definition of the operator trace: \(\coprod_ pEnd \Lambda^ pV\to R\) this operator is an algebra homomorphism. This fact is used to derive, among others, the Newton identities relating the elementary invariants and the sum-of- powers invariants of endomorphisms A in End V.
exterior power, endomorphisms, Newton identities, direct sum, trace, invariants, Endomorphism rings; matrix rings, Other classes of modules and ideals in associative algebras, algebra homomorphism, Vector and tensor algebra, theory of invariants, Automorphisms and endomorphisms
exterior power, endomorphisms, Newton identities, direct sum, trace, invariants, Endomorphism rings; matrix rings, Other classes of modules and ideals in associative algebras, algebra homomorphism, Vector and tensor algebra, theory of invariants, Automorphisms and endomorphisms
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