the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

Current researches have showed that N3, N5-diaryl-2, 6-dimethyl -1, 4-dihydropyrine-3, 5- dicarboxamide analogues demonstrate notable anti-tubercular activity. In this study, Hantzsch condensation was used to design and synthesize new analogues of dihydropyridine (DHP). Different diary carboxamides were inserted at positions 3 and 5 of the DHP ring. 4(5)-chloro-2-ethyl-5(4)-imidazolyl moiety wa...

In order to establish an estimate of the ages of large Pacific madrone (Arbutus menziesii) trees growing atop the bluffs on Magnolia Boulevard in Seattle, Washington, I obtained stump-discs from madrones cut by the Seattle Parks Department in June 1994. Each disc was sectioned into smaller pieces to allow processing with standard woodworking techniques. After initial processing, each slab was s...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

in this work, we investigate the transfer of some homological properties from a ring $r$ to its amalgamated duplication along some ideal $i$ of $r$ $rbowtie i$, and then generate new and original families of rings with these properties.

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...