vengeance is developed in order to oblige the debtors to return their debts and to support those creditors who, for administration of justice, cannot deliver any acceptable document to the machinery of justice. the exercise of vengeance is applicable, sometimes by taking back the corpus of usurped property and some other times by taking an intervenient exchange. religious jurists have different...

a module is said to be $pi$-extending provided that every projection invariant submodule is essential in a direct summand of the module. in this paper, we focus on direct summands and indecomposable decompositions of $pi$-extending modules. to this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

It is shown that simple and coalitional strategy-proofness of a voting rule on the full unimodal domain of a convex idempotent interval space (X, I) are equivalent properties if (X, I) satisfies interval anti-exchange, a basic property also shared by a large class of convex geometries including -but not reducing totrees and linear geometries. Therefore, strategy-proof location problems in a vas...

Convex analysis” is developed for functions defined on integer lattice points. We investigate the class of functions which enjoy a variant of Steinitz’s exchange property. It includes linear functions on matroids, valuations on matroids (in the sense of Dress and Wenzel), and separable concave functions on the integral base polytope of submodular systems. It is shown that a function ω has the S...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.