… dimension for commutative rings. The valuation dimension is a measure of how far a
commutative ring … It is shown that a ring R with valuation dimension has finite uniform dimension. …

… All rings in this paper are commutative with unity and … [1977]),if 𝒫 is a ring property,we say
that a ring R is locally 𝒫 if R M … A ring R is a valuation ring if R is a uniserial module,and R is …

… that M / M n is uniserial or M / M n ≅ M / M k for all k ⩾ n (see Proposition 1.3). This yields
that … Noetherian module has uniserial dimension. We also show that a commutative ring R is …

… A module MR over a ring R is uniserial provided its submodules are linearly … ,ring with
Krull dimension one. In this paper, given that R is a serial ring with arbitrary Krull dimension we …

… If (R,M) is a local ring, then M is uniserial and so R is uniserial. Thus we can assume that
R … The uniform dimension of a module M, denoted udim(M), is defined to be n if there is an …

… if and only if the codominant dimension of each injective left R-… uniserial rings and show
that the codominant dimension, or equivalently, dominant dimension, is a strict function of the ring…

… In order to define uniserial dimension for modules over a ring \(R\), we first define, by transfinite
… Since all finitely generated modules over a commutative ring are Hopfian (see [10]), they …

… Let R be an algebra over a field K of finite dimension (more generally R is an artinian …
Commutative rings In this section we assume that R is a commutative ring. Then every cyclic hollow …

… dimension^n for modules are all equivalent (Theorem 5). In §2, first we attend to Nakayama's
theorem [15] that a ring R is uniserial … always holds for commutative rings (Proposition 11). …

… Markov and Tuganbaev 2018b) and the exterior algebra of a three-dimensional vector space
… Let A be a commutative ring and I an ideal of the ring R. Then the following conditions are …