In his 1795 essay ‘Toward Perpetual Peace’ the East-Prussian university metaphysician Immanuel Kant (1724-1804) named ‘Hugo Grotius, Pufendorf, Vattel’ as the ‘miserable comforters’ of the law of nations. This was a bon mot that became celebrated retrospectively, with the late-twentieth-century reception of Kant’s cosmopolitanism in political philosophy and international relations theory. In fo...

Introduction. L. Fuchs [2 ] has given for Noetherian rings a theory of the representation of an ideal as an intersection of primal ideals, the theory being in many ways analogous to the classical Noether theory. An ideal Q is primal if the elements not prime to Q form an ideal, necessarily prime, called the adjoint of Q. Primary ideals are necessarily primal, but not conversely. Analogous resul...

in this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in ag -groupoids. generalizing the concepts of (,q) -fuzzy bi-ideals (interior ideal), we define ( , ) k q -fuzzy bi-ideals, ( , ) k q -fuzzy left (right)-ideals and ( , ) k q -fuzzy interior ideals in ag -groupoids and discuss some fundamental aspects of these i...

Perpetual survival of Mycobacterium inside immunologically educated host is puzzle unsolved. The survival strategy breeds a stage at which the bacterium undergoes a metabolic arrest. They initiate lipid lunch by triggering glyoxylate shunt, a metabolic salvage strategy to combat hostile dynamics of host macrophase. Here, I highlight the plethora of functions that the enzyme of the pathway exhib...

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...

We prove that if a right distributive ring R, which has at least one completely prime ideal contained in the Jacobson radical, satisfies either a.c.c or d.c.c. on principal right annihilators, then the prime radical of R is the right singular ideal of R and is completely prime and nilpotent. These results generalize a theorem by Posner for right chain rings.