Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.

A ring with identity is said to be clean if every element can be written as a sum of a unit and an idempotent. The study of clean rings has been at the forefront of ring theory over the past decade. The theory of partially-ordered groups has a nice and long history and since there are several ways of relating a ring to a (unital) partially-ordered group it became apparent that there ought to be...

It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. It is shown that each indecomposable module over a commutative ring R satisfies a finite condition if and only if R P is an artinian valuation ring for each maximal prime ideal P. Commutative rings for which each indecomposable module has a local endomorphism ring are studied...

Using the most recent updated physics, calibrated solar models have been computed with the new thermonuclear reaction rates of NACRE, the recently available European compilation. Comparisons with models computed with the reaction rates of Caughlan & Fowler (1988) and of Adelberger et al. (1998) are made for global structure, expected neutrinos fluxes, chemical composition and sound speed profil...

Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type with , 1 α  , 2 and , 2  and have be...

A unitary commutative ring of characteristic 3 and 3-potent is called a 3-ring. We prove that every polynomial of a 3-ring is uniquely determined by its restriction on the subring {0, 1, 2} (the Verification Theorem). Then we establish an isomorphism between the category of 3-rings and the category of Post algebras of order 3.