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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