… of a weakly regular (right) module: A right i?-module M is called a weakly regular module if
mEHom5 (M, M)(m)HomR(My … A right i?-module M is called a weakly regular module (abbr. w. …

… as rings over which each module is semisimple. In this paper, we consider rings over which
each module is weakly regular. … Then there exists a non-weakly regular module over R. …

… Since h(N) is a finitely generated submodule of the regular module L, the module h(N) is a
direct summand of L. Therefore, Q + N = Q ⊕ h(N) is a direct summand of M. By 1.16(1), there …

… and copure-injectively poor modules are given. Rings over which every module is weakly
poor … A ring over which there is a cyclic projective weakly poor module is proved to be weakly …

… module is weakly regular. For commutative R , this yields the desired result; namely, any
projective V-module is regular… (i) A projective weakly regular module need not be an /77-module…

… A[G]-module M (8)A|G| is weakly regular. In the latter part of this paper, we deal with submodules,
factor modules, extensions and direct products of weakly regular modules. Throughout …

… or image-direct module, then M is weakly-morphic if and only if each element of \(S_M\) is
regular as an element of S (see Theorem 15); if M is a weakly-morphic module over an integral …

… regular algebra is weakly regular. We know that an algebra A is regular if and only if for every
right A-module … concept of quasi dimension of weakly regular algebras and study its some …

… One property of weakly F-regular rings we will use is that they are reduced. In fact, it is not
hard … (unless d = 1), we can interpret L as a graded R module by suitably regrading R. Namely, …

… direct sums of weakly-injective right modules are weakly-injective if and only if every cyclic
right R-module has finite univorm dimen sion. We also discuss right weakly-semisimple rings (…