共查询到20条相似文献,搜索用时 46 毫秒
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Wei Hu Xiu-Hua Luo Bao-Lin Xiong Guodong Zhou 《Journal of Pure and Applied Algebra》2019,223(3):1014-1039
We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras A and B, we use the special monomorphism category to describe some Gorenstein projective bimodules over the tensor product of A and B. If one of the two algebras is Gorenstein, we give a sufficient and necessary condition for being the category of all Gorenstein projective bimodules. In addition, if both A and B are Gorenstein, we can describe the category of all Gorenstein projective bimodules via filtration categories. Similarly, in this case, we get the same result for infinitely generated Gorenstein projective bimodules. 相似文献
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Jean-Simon Pacaud Lemay 《Journal of Pure and Applied Algebra》2019,223(10):4191-4225
Differential categories were introduced by Blute, Cockett, and Seely as categorical models of differential linear logic and have since led to abstract formulations of many notions involving differentiation such as the directional derivative, differential forms, smooth manifolds, De Rham cohomology, etc. In this paper we study the generalization of differential algebras to the context of differential categories by introducing -differential algebras, which can be seen as special cases of Blute, Lucyshyn-Wright, and O'Neill's notion of -derivations. As such, -differential algebras are axiomatized by the chain rule and as a consequence we obtain both the higher-order Leibniz rule and the Faà di Bruno formula for the higher-order chain rule. We also construct both free and cofree -differential algebras for suitable codifferential categories and discuss power series of -algebras. 相似文献
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Rosalie Iemhoff 《Annals of Pure and Applied Logic》2019,170(11):102711
This paper presents a uniform and modular method to prove uniform interpolation for several intermediate and intuitionistic modal logics. The proof-theoretic method uses sequent calculi that are extensions of the terminating sequent calculus for intuitionistic propositional logic. It is shown that whenever the rules in a calculus satisfy certain structural properties, the corresponding logic has uniform interpolation. It follows that the intuitionistic versions of and (without the diamond operator) have uniform interpolation. It also follows that no intermediate or intuitionistic modal logic without uniform interpolation has a sequent calculus satisfying those structural properties, thereby establishing that except for the seven intermediate logics that have uniform interpolation, no intermediate logic has such a sequent calculus. 相似文献
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Guram Bezhanishvili Nick Bezhanishvili Joel Lucero-Bryan Jan van Mill 《Annals of Pure and Applied Logic》2019,170(5):558-577
For a topological space X, let be the modal logic of X where □ is interpreted as interior (and hence ◇ as closure) in X. It was shown in [3] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, (), and their intersections arise as for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer to [3, Question 6.2]. On the other hand, we show that a scattered Stone space that is in addition hereditarily paracompact does not give rise to a new logic; namely we show that the logic of such a space is either S4.Grz or for some . In fact, we prove this result for any scattered locally compact open hereditarily collectionwise normal and open hereditarily strongly zero-dimensional space. 相似文献