The Ideal Extension in Quantales
Bin Zhao · Mohu xitong yu shuxue · 2009
In this paper,the properties of Id(Q) are discussed.A condition that every ideal of a quantale Q is semiprime ideal is given,if the quantale Q is commutative.The concept of ideal extension is introduced.We get that some propositions concerning ordered semigroup still hold for ideal extension in a quantale.A quantic congruence is constructed by the ideal extension.The quantic quotient induced by the congruence is frame and its concrete structure is found,if the original ideal is prime ideal.