Nuclei and applications to star, semistar, and semiprime operations
Abstract
We show that the theory of quantales and quantic nuclei motivate new results on star operations, semistar operations, semiprime operations, ideal systems, and module systems, and conversely the latter theories motivate new results on quantales and quantic nuclei. Results include representation theorems for precoherent prequantales and multiplicative semilattices; characterizations of the simple prequantales; and a generalization to the setting of precoherent quantales of the construction of the largest finite type semistar operation and the largest stable semistar operation smaller than a given semistar operation.
Keywords
Cite
@article{arxiv.1505.06433,
title = {Nuclei and applications to star, semistar, and semiprime operations},
author = {Jesse Elliott},
journal= {arXiv preprint arXiv:1505.06433},
year = {2015}
}
Comments
This is a substantial reworking, with a new title, of a previously posted paper arXiv:1101.2462 "Prequantales and applications to semistar operations and module systems."