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Descending chains of semistar operations. (arXiv:1711.05399v1 [math.AC])
来源于:arXiv
A class of integer-valued functions defined on the set of ideals of an
integral domain $R$ is investigated. We show that this class of functions,
which we call ideal valuations, are in one-to-one correspondence with countable
descending chains of finite type, stable semistar operations with largest
element equal to the $e$-operation. We use this class of functions to recover
familiar semistar operations such as the $w$-operation and to give a solution
to a conjecture by Chapman and Glaz when the ring is a valuation domain. 查看全文>>