Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of endowed with a bracket. In this work, we provide study morphisms double algebras, which relate to the $H_0$-Poisson structures Crawley-Boevey. We prove in particular that algebra structure defined for an arbitrary quiver only depends upon seen undirected graph, up isomorphism. derive from our result...

The Kodaira-Spencer map is a component of the connection ∇. In particular, this implies that if κs 6= 0 then the connection∇ is nontrivial with respect to the Hodge decomposition. Various Hodge-theory facts imply that the global monodromy must be nontrivial in this case. We can be a bit more precise: if u ∈ V p,q is a vector such that κs(v)(u) 6= 0 for some tangent vector v ∈ T (S)s, then u can...

in this paper, a commutative semigroup will be written as a disjoint :union: of its cancellative subsemigroups. based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

We prove that a Tate construction A〈u1, . . . , un | ∂(ui) = zi〉 over a DG algebra A, on cycles z1, . . . , zn in A> 1, is acyclic if and only the map of graded-commutative algebras H0(A)[y1, . . . , yn] → H(A), with yi 7→ cls(zi), is an isomorphism. This is used to establish that if a large homomorphism R → S has an acyclic closure R〈U〉 with sup{i | Ui 6= ∅} = s < ∞, then s is either 1 or an e...

It is proved that every commutative ring whose RD-injective modules are Σ-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively th...

New developments on non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a scalar field is coupled to a Chern Simons gauge field, a geometrical phase emerges for vortex like solutions, transformed by Galilei boosts. Non commutative solitons finite actio...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

In this paper we develop a Sz.-Nagy-Foiaş type theory of characteristic functions and functional models on noncommutative domains varieties in $$B(\mathcal{H})^n$$ , where $$B(\mathcal{H})$$ is the algebra all bounded linear operators Hilbert space $$\mathcal{H}$$ associated with admissible free holomorphic for operator model theory. This includes, particular, large class commutative . case, ar...