THE BANASCHEWSKI-SIOEN NUCLEUS ON AN ALGEBRAIC FRAME

In their construction of the Stone-\v{C}ech compactification using only ring ideals (as opposed to \ell-ideals), Banaschewski and Sioen define a certain nucleus on the coherent frame \Rid(A) of radical ideals of a commutative ring A. In this paper we extend this nucleus to any algebraic frame that has a dense compact element and in which the meet of two compact elements is compact. Of course, not every such algebraic frame is coherent, so the extension is indeed a genuine extension. We then study some properties of this nucleus which are not considered by Banaschewski and Sioen.

کلیدواژه ها:

Algebraic frame ، Commutative rings ، nucleus and sublocale