ON MODULES AND MATRIX RINGS WITH SIP-EXTENDING
نویسندگان
چکیده
منابع مشابه
On Ads-modules with the SIP
The class of ads modules with the SIP (briefly, $SA$-modules) is studied. Various conditions for a module to be $SA$-module are given. It is proved that for a quasi-continuous module $M$, $M$ is a UC-module if and only if $M$ is an $SA$-module. Also, it is proved that the direct sum of two $SA$-modules as $R$-modules is an $SA$-module when $R$ is the sum of the annihilators of thes...
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A torsion theory is called differential (higher differential) if a derivation (higher derivation) can be extended from any module to the module of quotients corresponding to the torsion theory. We study conditions equivalent to higher differentiability of a torsion theory. It is known that the Lambek, Goldie and any perfect torsion theories are differential. We show that these classes of torsio...
متن کاملon ads-modules with the sip
the class of ads modules with the sip (briefly, $sa$-modules) is studied. various conditions for a module to be $sa$-module are given. it is proved that for a quasi-continuous module $m$, $m$ is a uc-module if and only if $m$ is an $sa$-module. also, it is proved that the direct sum of two $sa$-modules as $r$-modules is an $sa$-module when $r$ is the sum of the annihilators of these...
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It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2007
ISSN: 1027-5487
DOI: 10.11650/twjm/1500404800