Shunqin Wang, Bin Zhao
Abstract
In this paper, a prime ideal and a weakly prime ideal of a quantale are defined. The relation between them is discussed. A necessary and sufficient condition under which a ideal of a quantale is (weakly) prime is obtained. At last we get that some conclusion concerning ordered semigroup still (hold) for a (weakly) prime ideal of a quantale.
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In this paper, a prime ideal and a weakly prime ideal of a quantale are defined. The relation between them is discussed. A necessary and sufficient condition under which a ideal of a quantale is (weakly) prime is obtained. At last we get that some conclusion concerning ordered semigroup still (hold) for a (weakly) prime ideal of a quantale.
Key concepts: Mathematics, Ideal (ethics), Prime (order theory), Minimal ideal, Semigroup, Prime ideal, Radical of an ideal, Pure mathematics