We describe a construction of fuzzy spaces which approximate projective toric varieties. The construction uses the canonical embedding of such varieties into a complex projective space: The algebra of fuzzy functions on a toric variety is obtained by a restriction of the fuzzy algebra of functions on the complex projective space appearing in the embedding. We give several explicit examples for ...

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules, which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These last three classes of modules give us a new characterization of the first modules, and confirm that there is an analogy between the notion of “Gorenstein projective, injective, and flat modules”and the no...

It is known that the partition function and correlators of the two-dimensional topological field theory GK(N)/GK(N) on the Riemann surface Σg,s is given by Verlinde numbers, dim(Vg,s,K) and that the large K limit of dim(Vg,s,K) gives Vol(Ms), the volume of the moduli space of flat connections of gauge group G(N) on Σg,s, up to a power of K. Given this relationship, we complete the computation o...

If R is a ring of coefficients and G a finite group, then a flat RG-module which is projective as an R-module is necessarily projective as an RG-module. More generally, if H is a subgroup of finite index in an arbitrary group Γ, then a flat RΓmodule which is projective as an RH-module is necessarily projective as an RΓ-module. This follows from a generalization of the first theorem to modules o...

the aim of the present paper is to define and study (ic)$lm$-fuzzytopological spaces, a generalization of (weakly) induced $lm$-fuzzytopological spaces. we discuss the basic properties of(ic)$lm$-fuzzy topological spaces, and introduce the notions ofinterior (ic)-fication and exterior (ic)-fication of $lm$-fuzzytopologies and prove that {bf iclm-ftop} (the category of(ic)$lm$-fuzzy topological ...

In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mapping...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

Gupta and Ray (Fuzzy Sets and Systems 54 (1993) 191) introduced the notion of fuzzy projective planes. We show that an old theorem of Dembowski classi$es all $nite fuzzy projective planes, that the examples in Gupta and Ray (Fuzzy Sets and Systems 54 (1993) 191) arise from ordinary projective planes and have much easier descriptions that can easily be generalized, and that there exist fuzzy pro...

In this paper, we study the relation between m-strongly Gorenstein projective (resp. injective) modules and n-strongly Gorenstein projective (resp. injective) modules whenever m 6= n, and the homological behavior of n-strongly Gorenstein projective (resp. injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Goren...

We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries in Chern-Simons and topological BF theories is formulated.