A theorem about coprime action

A Theorem About Uniform Distribution

A Theorem about Random Fields

Averintsev [1] and Spitzer [2] proved that the class of Markov fields is identical to the class of Gibbs ensembles when the domain is a finite subset of the cubic lattice and each site may be in either of two given states. Hammersley and Clifford [3] proved the same result for the more general case when the domain is the set of sites of an arbitrary finite graph and the number of possible state...

Coprime Comodules and Coprime Corings

Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely coprime corings (coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate their relatio...

Fully Coprime Comodules and Fully Coprime Corings

Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate t...

A Note about a Burton Keane's Theorem

In BURTON-KEANE'S structural paper 1] a situation has not been lightened, such that the proof of their result about the topological structure of ribbons in the two-dimensional site percolation has a gap. We introduce the connuent zone notion and prove, using Burton-Keane's arguments , the almost surely absence of these zones (This completes the proof of the topological structure of ribbons anno...