Results 91 to 100 of about 310,219 (199)
Superstability, noetherian rings and pure-semisimple rings
Annals of Pure and Applied Logic, 2021 We uncover a connection between the model-theoretic notion of superstability and that of noetherian rings and pure-semisimple rings. We characterize noetherian rings via superstability of the class of left modules with embeddings. $\mathbf{Theorem.}$ For a ring $R$ the following are equivalent. - $R$ is left noetherian.
openaire +2 more sources
Noncommutative piecewise Noetherian rings
, 2011 The concept of reduced rank has been a useful tool in studying Noetherian rings, orders in Artinian rings, and rings with Krull dimension. These classes of rings have been generalized, in the commutative setting, to a class of rings called piecewise ...
Pearson, Abigail C.
core
The Noetherian property for quotient rings of infinite polynomial rings
, 1979 Let X be an infinite set of indeterminates over the commutative Noetherian ring R with identity. We prove that the quotient ring of R [ X ] R[X] with respect to the multiplicative system of polynomials of ...
William Heinzer, Robert Gilmer
core +1 more source
, 2012 Noetherian Rings have their own unique and distinguishing properties. Emmy Noether, the daughter and sister of Mathematicians, came to study a concentration of Abstract Algebra, Ring Theory, Group Theory, and much more during the 1920\u27s; this finally ...
Walker, Shaine Donnie
core +1 more source
Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum. [PDF]
Math Ann, 2023 Bik A, Danelon A, Draisma J.
europepmc +1 more source
Embedding Noetherian Rings in Artinian Rings
Journal of Algebra, 2001 A well-known theorem of \textit{A. H. Schofield} [``Representation of rings over skew fields'', Lond. Math. Soc. Lect. Note Ser. 92, CUP, Cambridge (1985; Zbl 0571.16001)] asserts that an algebra \(A\) over a field can be embedded in a right Artinian ring if and only if there is a faithful Sylvester rank function on finitely presented \(A\)-modules. By
openaire +1 more source
Certain Artinian Rings are Noetherian
, 1972 Throughout this paper the word “ring” will mean an associative ring which need not have an identity element. There are Artinian rings which are not Noetherian, for example C(p∞) with zero
Robert C. Shock
core +1 more source
Constructions over localizations of rings
Le Matematiche, 1987 In this paper we construct a category of effective noetherian rings in which linear equations can be “solved”. This category is closed with respect to some important constructions like trascendental extensions, quotientations, finite products and ...
Alessandro Logar
doaj
A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings
Journal of MathematicsIn this paper, we introduce the concept of weakly semiprime ideals and weakly n-systems in noncommutative rings. We establish the equivalence between an ideal P being a weakly semiprime ideal and R−P being a weakly n-system.
Alaa Abouhalaka
doaj +1 more source
, 1984 A module M is called a serial module if the family of its submodules is linearly ordered under inclusion. A ring R is said to be serial if RR as well as RR are finite direct sums of serial modules. Nakayama [8] started the study of artinian serial rings,
Surjeet Singh
core +1 more source