A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute. By SRC factorization, Borooah, Diesl, and Dorsey [3] completely determined when Mn(R) over a commutative local ring R is strongly clean. We generalize the notion of SRC factorization to commutative rings, prove that commutative n-SRC rings (n ≥ 2) are precisely the commutative local ring...

The critical properties of the real φ scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a finite matrix (non–commutative) approximation of the algebra of functions on the usual two dimensional sphere. It is also one of the simplest examples of a non–commutative space to study field theory on. Aside from the usual disordered and uniform phases present in the co...

We are studying the dynamics of a one-dimensional field in a noncommutative Euclidean space. The non-commutative space we consider is the one that emerges in the context of three dimensional Euclidean quantum gravity: it is a deformation of the classical Euclidean space E3 and the Planck length lP plays the role of the deformation parameter. The field is interpreted as a particle which evolves ...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

The new generalization of the gauge interaction for the bosonic strings is found. We consider some quasi-equivariant maps from the space of metrics on the worldsheet to the space of n-tuples of oneand two-dimensional loops. The two-dimensional case is based on the cylinders interacted with a path space connection. The special 2-gauge string model is formulated using two 1-connections, nonabelia...

We generalize recent results by G.A. Freiman, M. Herzog and coauthors on the structure theory of product-sets from the context of linearly (i.e., strictly and totally) ordered groups to linearly ordered semigroups. In particular, we find that if S is a finite subset of a linearly ordered semigroup generating a nonabelian subsemigroup, then |S2| ≥ 3 |S| − 2. On the road to this goal, we also pro...

We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field theories, with or without supersymmetry. The formalism has a number of intuitive advantages. First it makes clear the appearance of new degrees of freedom in th...

We consider the Standard Model on a non-commutative space and expand the action in the non-commutativity parameter θ . No new particles are introduced, the structure group is SU(3)×SU(2)×U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard Model. At leading order in θ we find new vertices which are absent in the Standard Model on commutative ...

In this survey we present the appearance of some combinatorial notions in quantum field theory. We first focus on graph polynomials (the Tutte polynomial and its multivariate version) and their relation with the parametric representation of the commutative Φ field theory. We then generalize this to ribbon graphs and present the relation of the Bollobás–Riordan polynomial with the parametric rep...

Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics. Souriau's construction applied to the two-parameter central extension of the planar Galilei group lead to the " exotic " particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical mod...