an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

Order unit spaces with comparability and spectrality properties as introduced by Foulis are studied. We define continuous functional calculus for order the property Borel spectral spaces. Applying conditions of Alfsen Schultz, we characterize that JB-algebras. also prove a characterization Rickart JB-algebras those which every maximal associative subalgebra is monotone σ-complete, extending an ...

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3. N. Dunford and B. J. Pettis, Linear operators on summable functions, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 323-392. 4. O. Nikodym, Sur une generalisation des integrates de M. Radon, Fund. Math, vol. 15 (1930) pp. 137-179. 5. R. S. Phillips, Integration in convex linear topological space, Trans. Amer. Math. Soc. vol. 48 (1940) pp. 516-540. 6. C. E. Rickart, Integration in a convex linear...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...