Results 41 to 50 of about 306,524 (177)
Torsion pairs via the Ziegler spectrum
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract We establish a bijection between torsion pairs in the category of finite‐dimensional modules over a finite‐dimensional algebra A$A$ and pairs (Z,I)$(\mathcal {Z},\mathcal {I})$ formed by a closed rigid set Z$\mathcal {Z}$ in the Ziegler spectrum of A$A$ and a set I$\mathcal {I}$ of indecomposable injective A$A$‐modules. This is as an extension
Lidia Angeleri Hügel +2 more
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Whitehead groups of exchange rings with primitive factors artinian
International Journal of Mathematics and Mathematical Sciences, 2001 We show that if R is an exchange ring with primitive factors artinian then K1(R)≅U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1|a,b∈R with 1+ab∈U(R)}.
Huanyin Chen, Fu-an Li
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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
From points to complexes: A concept of unexpectedness for simplicial complexes
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract In 2018, Cook, Harbourne, Migliore, and Nagel introduced the concept of unexpected hypersurfaces, which connects the study of Lefschetz properties of Artinian algebras defined by powers of linear forms to a family of interpolation problems.
Thiago Holleben
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Ural Mathematical JournalIn 1996, the first author defined analogs of the concepts of complete (divisible), reduced, and periodic abelian groups, well-known in the theory of abelian groups, for arbitrary varieties of algebras. In 2021, the first author proposed a modification of
Leonid M. Martynov, Tatiana V. Pavlova
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Classification of rings with toroidal annihilating-ideal graph
Communications in Combinatorics and Optimization, 2018 Let $R$ be a non-domain commutative ring with identity and $\mathbb{A}^*(R)$ be the set of non-zero ideals with non-zero annihilators. We call an ideal $I_1$ of $R$, an \textit{annihilating-ideal} if there exists a non-zero ideal $I_2$ of $R$ such ...
K. Selvakumar +1 more
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A classification of Prüfer domains of integer‐valued polynomials on algebras
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Let D$D$ be an integrally closed domain with quotient field K$K$ and A$A$ a torsion‐free D$D$‐algebra that is finitely generated as a D$D$‐module and such that A∩K=D$A\cap K=D$. We give a complete classification of those D$D$ and A$A$ for which the ring IntK(A)={f∈K[X]∣f(A)⊆A}$\textnormal {Int}_K(A)=\lbrace f\in K[X] \mid f(A)\subseteq A ...
Giulio Peruginelli, Nicholas J. Werner
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Characterization and examples of commutative iso-Artinian rings [PDF]
Noetherian rings have played a fundamental role in commutative algebra, algebraic number theory, and algebraic geometry. Along with their dual, Artinian rings, they have many generalizations, including the notions of iso-Noetherian and iso-Artinian rings.
Daneshvar, Asghar, Divaani-Aazar, Kamran
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, 2002 Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
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The sum-annihilating essential ideal graph of a commutative ring
Communications in Combinatorics and Optimization, 2016 Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$ is called an annihilating ideal if there exists $r\in R\setminus \{0\}$ such that $Ir=(0)$ and an ideal $I$ of $R$ is called an essential ideal if $I$ has non-zero ...
A. Alilou, J. Amjadi
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