Non-pointed Exactness, Radicals, Closure Operators
نویسندگان
چکیده
In this paper it is shown how non-pointed exactness provides a framework which allows a simple categorical treatment of the basics of KuroshAmitsur radical theory in the non-pointed case. This is made possible by a new approach to semi-exactness, in the sense of the first author, using adjoint functors. This framework also reveals how categorical closure operators arise as radical theories.
منابع مشابه
Torsion theories and radicals in normal categories
We introduce a relativized notion of (semi)normalcy for categories that come equipped with a proper stable factorization system, and we use radicals and normal closure operators in order to study torsion theories in such categories. Our results generalize and complement recent studies in the realm of semi-abelian and, in part, homological categories. In particular, we characterize both, torsion...
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 کاملNear Rough and Near Exact Subgraphs in Gm-Closure Spaces
The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition...
متن کاملCHARACTERIZATION OF L-FUZZIFYING MATROIDS BY L-FUZZIFYING CLOSURE OPERATORS
An L-fuzzifying matroid is a pair (E, I), where I is a map from2E to L satisfying three axioms. In this paper, the notion of closure operatorsin matroid theory is generalized to an L-fuzzy setting and called L-fuzzifyingclosure operators. It is proved that there exists a one-to-one correspondencebetween L-fuzzifying matroids and their L-fuzzifying closure operators.
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 کامل