Modules whose countably generated submodules are epimorphic images
Which fields have no maximal subrings ?
On the functionally countable subalgebra of C(X)
Erratum to: "C(X) vs. C(X) modulo its socle" (Colloq. Math. 111 (2008), 315-336)
C(X) vs. C(X) modulo its socle
Let be the socle of C(X). It is shown that each prime ideal in is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential...
Erratum to "On rings with a unique proper essential right ideal" (Fund. Math. 183 (2004), 229-244)
On rings with a unique proper essential right ideal
Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and is Artin semisimple...
Page 1