… of Azumaya algebras over a commutative ring k consists of all … , a right quotient ring Q is a
ring R such that: (1) Each regular … and b regular, then there exists a₁, b₁ € R, with b₁ regular …

… But then N is a large Jónsson R-module of regular cardinality, contradicting Corollary 22. …
modules over an arbitrary commutative ring. To do this, we will need the following two lemmas. …

… 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. …

… module, depends substantially on the underlying ring R. Negative realization results are known
for right noetherian and for commutative rings: if … as ar-invariant of a uniform module, [18, …

… Let R be a commutative ring with 1 and M an R-module. If r : M | M ~ R is an R-module …
As M is a maximal CM-module over a regular ring M must be free, and thus by lemma 2.1 M …

… is a commutative ring with identity and all modules are unital. … R be a regular ring, I an
ideal of R and M an R-module with IM=… an R-module if and only if M is injectίve as an Rf I -module. …

… ring A is said to be regular if a ∈ aAa for every element a of A. It is well known that a ring A is
regular ⇐⇒ A is a regular right A-module … D In the case of modules over commutative rings, …

… From 1966 on, coherence in commutative rings became a … rings and the research done in
other areas of commutative algebra. … approach to some results in regular rings. The structure of …

… commutative rings such as Noetherian rings, reduced rings, Rickart rings, semi-Artinian rings
and self-injective rings, … A ring R is said to be a von Neumann regular ring if for every a ∈ R …