… ring having nonzero socle is a regular ring and so S being a ring direct sum of regular rings
is a regular ring… If V denotes the maximal regular ideal of R [3], then iScF since S is a regular …

… of V and the F-module M a Jônsson α generated ideal of a ring R [14, p. 2]. We note that
this in fact gives for α a regular cardinal a Jônsson α-generated module or ideal for which the …

… Then the question is: is a projective module P over a commutative ring R a regular module
if and only if it is a ^-module? In [9] Ware proved the … We call a module P over a ring R …

… a general commutative ring is extended from a separable algebra over a … commutative ring,
and, in § 2, we shall prove that, in case J? is a commutative ring included in a semi-local ring, …

… These modules will be called temporarils "nice modules" and we prove that nice modules
actually are locally cyclic modules. For any locally cyclic module, we get thus a spectrum and …

… class of commutative noetherian DG-rings which generalizes the class of regular local rings.
… its degree 0 part which is simply the surjection of commutative rings π A 0 : A 0 → H 0 ( A ) . …

… ring (a commutative ring in which all finitely generated ideals are principal), and let M be a
finitely generated R-module. We … module over a principal ideal ring or a von Neumann regular …

… fact to prove that any commutative regular ring has an algebraic … to commutative semiprime
rings and abelian regular rings. … A commutative ring is semiprime if its prime radical is {0}, or …

… if r is a regular element of R, then the R-module R / r R has projective dimension at most one,
hence it is projective. So r R = e R for some idempotent element e ∈ R . Since r is regular it …

… von Neumann) regular ring. The first … regular iff every principal left ideal is the left annihilator
of an element of A. It is well-known that a commutative ring is regular iff every simple module …