Closure Systems and Closure Operations in Dedekind
نویسندگان
چکیده
The concepts of closure systems and closure operations in lattice theory are basic and applied to many fields in mathematics and theoretical computer science. In this paper authors find out a suitable definition of closure systems in Dedekind categories, and thereby give an equivalence proof for closure systems and closure operations in Dedekind categories.
منابع مشابه
Topics on the Ratliff-Rush Closure of an Ideal
Introduction Let be a Noetherian ring with unity and be a regular ideal of , that is, contains a nonzerodivisor. Let . Then . The :union: of this family, , is an interesting ideal first studied by Ratliff and Rush in [15]. The Ratliff-Rush closure of is defined by . A regular ideal for which is called Ratliff-Rush ideal. The present paper, reviews some of the known prop...
متن کاملFrom torsion theories to closure operators and factorization systems
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
متن کاملM-FUZZIFYING MATROIDS INDUCED BY M-FUZZIFYING CLOSURE OPERATORS
In this paper, the notion of closure operators of matroids is generalized to fuzzy setting which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...
متن کاملP-CLOSURE IN PSEUDO BCI-ALGEBRAS
In this paper, for any non-empty subset C of a pseudo BCI-algebra X, the concept of p-closure of C, denoted by C(pc), is introduced and some related properties are investigated. Applying this concept, a characterization of the minimal elements of X is given. It is proved that C(pc) is the least closed pseudo BCI-ideal of X containing C and K(X) for any ideal C of X...
متن کاملCategories isomorphic to the category of $L$-fuzzy closure system spaces
In this paper, new definitions of $L$-fuzzy closure operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood spaces, the category of ...
متن کامل