Non-commutative deformations and quasi-coherent modules

On quasi-zero divisor graphs of non-commutative rings

Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...

Quasi-Particles in Non-Commutative Field Theory

After a short introduction to the UV/IR mixing in non-commutative field theories we review the properties of scalar quasi-particles in noncommutative supersymmetric gauge theories at finite temperature. In particular we discuss the appearance of super-luminous wave propagation. 1 Talk given at NATO ARW ”Non-Commutative Structures in Mathematics and Physics”, Kyiv 24-27 Sep. 2000

Quasi-Exact Sequence and Finitely Presented Modules

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

Extensions of Baer and quasi-Baer modules

Projective Modules over Higher-dimensional Non-commutative Tori

The non-commutative tori provide probably the most accessible interesting examples of non-commutative differentiable manifolds. We can identify an ordinary n-torus rn with its algebra, C(rn), of continuous complex-valued functions under pointwise multiplication. But C(rn) is the universal C*-algebra generated by n commuting unitary operators. By definition, [15, 16, 50], a non-commutative n-tor...