Closure Operations and Nuclei
J. Elliott
2019
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Springer Monographs in Mathematics
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Semantic Scholar
Key Takeaway Key Takeaway: Closure operations on commutative rings can be applied to nuclei on ordered magmas, advancing our understanding of order theory and its implications for nuclei.
Abstract
This chapter generalizes many of the requisite facts on semistar, star, and semiprime operations on commutative rings employed in Chapters 1– 4 to nuclei on ordered magmas satisfying various algebro-order-theoretic hypotheses. This serves to situate the theories of semistar, star, and semiprime operations on commutative rings in the broader contexts of closure operations, order theory, and the theories of ordered monoids, quantales, and multiplicative lattices.
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