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.
scientific article; zbMATH DE number 3977211