We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of indecomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko states that the category of reflexive toric sheaves is equivalent to the category of vector spaces together with a certain family of filtrations. Within th...

We study the following question: Given two semidualizing complexes B and C over a commutative noetherian ring R, does the vanishing of Ext R (B, C) for n ≫ 0 imply that B is C-reflexive? This question is a natural generalization of one studied by Avramov, Buchweitz, and Şega. We begin by providing conditions equivalent to B being C-reflexive, each of which is slightly stronger than the conditio...

We give a proper definition of the multiplicative structure following rings: Cox ring invertible sheaves on general algebraic stack; rank one reflexive normal and excellent stack. show that such rings always exist establish its (non-)uniqueness in terms an Ext-group. Moreover, we compare this with classical construction variety. Finally, application to theory Mori dream stacks.

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

It is well known that the Chern classes ci of a rank n vector bundle on P N , generated by global sections, are non-negative if i ≤ n and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers ci with i ≥ 4 can be arbitrarily negative for reflexive sheaves of any rank; on the contrary fo...

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetr...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To noncommutative hypersurfaces, which are important objects algebraic geometry, we introduce a notion factorization for an arbitrary nonzero non-unit element ring. First show that the category graded invariant under operation called twist (this result generalization by Cassidy-Conner-Kirkman-Moore). Then g...

Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for Banach spaces involving a cylindrical Wiener process as integrator and an operator-valued stochastic process as integrand is defined. Basic properties of this integral are stated and proved. A class o...