Invertibility of multiplication modules All rings are commutative with 1 and all modules are unital. Let R be a ring and M an R-module. M is called multiplication if for each submodule N of M, N=IM for some ideal I of R. Multiplication modules have recently received considerable attention during the last twenty years. In this talk we give the de nition of invertible submodules as a natural gene...

Given a finite tensor category $\mathcal {C}$ , we prove that modified trace on the ideal of projective objects can be obtained from suitable trivialization Nakayama functor as right -module functor. Using result Costello, this allows us to associate any equipped with such chain complex valued topological conformal field theory, theory. The theory topologically describes trace, Hattori-Stalling...

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

Assuming that B is a full A∞-subcategory of a unital A∞-category C we construct the quotient unital A∞-category D =‘C/B’. It represents the A u ∞-2-functor A 7→ A∞(C,A)modB, which associates with a given unital A∞-category A the A∞-category of unital A∞-functors C → A, whose restriction to B is contractible. Namely, there is a unital A∞-functor e : C → D such that the composition B →֒ C e −→ D i...

We state that all Rota-Baxter operators of nonzero weight on Grassmann algebra over a field characteristic zero are projections subalgebra along another one. show the one-to-one correspondence between solutions associative Yang-Baxter equation and matrix $M_n(F)$ (joint with P. Kolesnikov). prove unital (alternative, Jordan) algebraic nilpotent. For an $A$, we introduce its new invariant rb-ind...

in this note, we characterize chebyshev subalgebras of unital jb-algebras. we exhibit that if b is chebyshev subalgebra of a unital jb-algebra a, then either b is a trivial subalgebra of a or a= h r .l, where h is a hilbert space