A J-ring is a ring R with the property that for every x in R there exists an integer n(x)>1 such that x x x n = ) ( , and a well-known theorem of Jacobson states that a Jring is necessarily commutative. With this as motivation, we define a generalized Jring to be a ring R with the property that for all x, y in R0 there exists integers 1 ) ( , 1 ) ( > = > = y m m x n n such that m n xy y x − is ...

Bases are exhibited for Kn, Kp,q, and Qd, and it is shown how each cycle of the various graphs can be built as a hierarchical ordered sum in which all of the partial sums are (simple) cycles with each cycle from either the basis or one of the hierarchically constructed cycle-sets meeting the partial sum of its predecessors in a nontrivial path. A property that holds for this “connected sum” of ...

We investigate the theories LA,LAP,∀LAP of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize Frege proofs. We give sentences separating quantified versions of these theories, and define a fragment ∃LA of ∀LAP in which we can interpret a weak theory V 1 of bounded arithmetic and carry out polynomial time reasoning about m...

After introducing commutativity concept and summarizing the relevant literature, this work is focused on the commutativity of feedback conjugates. It is already known that a linear time-varying differential system describing a single input-single output dynamical system is always commutative with its constant gain feedback pairs. In this article, it is proven that among the time-varying feedbac...

D We investigate the role of commutativity in query processing of linear recursion. We give a sufficient condition for two linear, function-free, and constant-free rules to commute. The condition depends on the form of the rules themselves. For a restricted class of rules, we show that the condition is necessary and sufficient and can be tested in polynomial time in the size of the rules. Using...

Constraint propagation is a general algorithmic approach for pruning the search space of a CSP. In a uniform way, K. R. Apt [1] has defined a computation as an iteration of reduction functions over a domain. In [2] he has also demonstrated the need for integrating static properties of reduction functions (commutativity and semi-commutativity) to design specialized algorithms such as AC3 and DAC...

To characterize categorical constraints associativity, commutativity and monoidality in the context of quasimonoidal categories, from a cohomological point of view, we define the notion of a parity (quasi)complex. Applied to groups gives non-abelian cohomology. The categorification functor from groups to monoidal categories provides the correspondence between the respective parity (quasi)comple...

In this work, we define the class preserving actor and commutativity degree of Lie crossed modules. Then, obtain some relations about these notions isoclinic

Constraint propagation is a general algorithmic approach for pruning the search space of a CSP. In a uniform way, K. R. Apt [1] has defined a computation as an iteration of reduction functions over a domain. In [2] he has also demonstrated the need for integrating static properties of reduction functions (commutativity and semi-commutativity) to design specialized algorithms such as AC3 and DAC...