Spacetime non-commutativity appears in string theory. In this paper, the non-commutativity in string theory is reviewed. At first we review that a Dp-brane is equivalent to a configuration of infinitely many D(p− 2)-branes. If we consider the worldvolume as that of the Dp-brane, coordinates of the Dp-brane is commutative. On the other hand if we deal with the worldvolume as that of the D(p− 2)-...

A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...

A ?semigroup is a semigroup whose lattice of congruences is a chain with respect to inclusion. Schein 9] and Tamura 11] have investigated commutative ?semigroups, Trotter 13] exponential, Nagy 4] weakly exponential and Bonzini and Cherubini Spoletini 2] nite ?semigroups. The pupose of the present paper is to investigate archimedean weakly commutative and H?commutative ?semigroups. 1 Weakly comm...

Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

In this article, we define a non-commutative deformation of the ”symplectic invariants” (introduced in [13]) of an algebraic hyperelliptical plane curve. The necessary condition for our definition to make sense is a Bethe ansatz. The commutative limit reduces to the symplectic invariants, i.e. algebraic geometry, and thus we define non-commutative deformations of some algebraic geometry quantit...

Duchamp, G. and D. Krob, On the partially commutative shuffle product, Theoretical Computer Science 96 (1992) 405410. We give recursive formulas that allow us to compute the partially commutative shuffle product of two partially commutative words.

The Hamiltonian (gauge) symmetry generators of non-local (gauge) theories are presented. The construction is based on the d + 1 dimensional space-time formulation of d dimensional non-local theories. The procedure is applied to U(1) space-time non-commutative gauge theory. In the Hamiltonian formalism the Hamiltonian and the gauge generator are constructed. The nilpotent BRST charge is also obt...

This paper explores ways of performing commutative tasks by N parties. Tasks are defined as commutative if the order at which parties perform tasks can be freely changed without affecting the final result. It is easy to see that arbitrary N-party commutative tasks cannot be completed in less than N − 1 basic time units. We conjecture that arbitrary N-party commutative tasks cannot be performed ...