An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...

poly (vinylpyrrolidone)-grafted silica as an organic-inorganic hybrid material was used as an effective heterogeneous polymeric cosolvent catalyst in organic reactions. this modified silica catalyzed nucleophilic displacement of alkyl halides for easy preparation of alkyl thiocyanates, alkyl cyanides, alkyl azides and alkyl aryl ethers. furthermore, the catalyst was applied for the conversion o...

The effect of alkyl substituents on the C-phenyl and/or the N-Phenyl ring of benzophenylhydroxamic acid on their molecular structure and hydrogen bonding has been investigated. The predominant configuration in CHCl3 is determined by steric and electronic effects. Substituents on the C-phenyl ring favor the cis configuration, while substituents in the N-phenyl ring favor a trans c...

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...

In this work we attempt to generalize our result in [6] [7] for real rings (not just von Neumann regular real rings). In other words we attempt to characterize and construct real closure ∗ of commutative unitary rings that are real. We also make some very interesting and significant discoveries regarding maximal partial orderings of rings, Baer rings and essentail extension of rings. The first ...

hot rolling of a large ring of titanium alloy (lrt) is a highly nonlinear incremental forming process with coupled mechanical and thermal behaviors (mtbs) which significantly affect microstructure and properties of the ring. the feed rate of idle roll and the rotational speed of driver roll have major effects on ovality of the ring. in this paper, the effects of these parameters on the ovality ...

Contents 1. Introduction 2. Real closed rings-a model theoretic tour 3. Computation of the z-radical in C(X) 4. A sentence in the language of rings separating continuous semi-algebraic from arbitrary continuous functions 5. Super real closed rings: Definition and basic properties 6. Υ-ideals 7. Localization of super real closed rings 8. Application: o-minimal structures on super real closed fie...

In this survey we determine an explicit set of generators of the maximal ideals in the ring R[x1, . . . , xn] of polynomials in n variables with real coefficients and give an easy analytic proof of the Bass-Vasershtein theorem on the Bass stable rank of R[x1, . . . , xn]. The ingredients of the proof stem from different publications by Coquand, Lombardi, Estes and Ohm. We conclude with a calcul...