in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

PURPOSE To psychophysically measure spherical and irregular aberrations in patients with various types of myopia correction. SETTING Laboratory of Experimental Ophthalmology, University of Groningen, Groningen, The Netherlands. METHODS Three groups of patients with low myopia correction (spectacles, soft contact lens, and Intacs) and 4 groups with high myopia correction (spectacles, rigid c...

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.

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...