… can be reformulated into a definition of a “regular” module (over a commutative ring) in
an obvious way, but it turns out that we obtain four distinct notions. (For a couple of simple …

… 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 ) . …

… results to topological modules over topological rings to obtain nontrivial regular closed and
regular open neighborhoods of zero. In particular, if M is a topological R-module and m ∗ ∈ …

… 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 …

… regular module in the sense [13]. Let 𝐴 be a commutative ring with 1 ≠ 0 and 𝑋 a multiplication
𝐴-module. … We say that an 𝐴-module 𝑋 as a strongly 𝜋regular module if for each 𝑥 ∈ 𝑋, …

… module over a commutative ring R, then the notions of strongly regular module and F-regular
module … We have given an example of a F-regular module which is not strongly regular. We …

… regular module over a commutative ring to a V N-regular module over a ring which is not
necessarily commutative… MV Nregular if aM = a2M where R is a commutative ring and M is an R-…

… of all regular elements of R) to replace the quotient field of a domain. However, it is worth
noting that some classical theorems on domains cannot be generalized to commutative rings …

… additive group structure on a commutative ring has little importance. … -commutative rings
and their modules, stressing the difference with what happens in the case of commutative rings. …

… Accordingly, structure of virtually semisimple modules over commutative rings … module
M over a commutative domain R is virtually regular if and only if M ∼ = N ⊕ R for some R-module …