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Let $R$ be a ring. We recall that $R$ is called a near pseudo-valuation ring if every minimal prime ideal of $R$ is strongly prime. Let now $σ$ be an automorphism of $R$ and $δ$ a $σ$ -derivation of $R$ . Then $R$ is said to be an almost $δ$ -divided ring if every minimal prime ideal of $R$ is $δ$ -divided. Let $R$ be a Noetherian ring which is also an algebra over $ℚ$ ( $ℚ$ is the field of rational numbers). Let $σ$ be an automorphism of $R$ such that $R$ is a $σ (*)$ -ring and $δ$ a $σ$ -derivation of $R$ such that $σ (δ (a)) = δ (σ (a))$ for all $a \in R$ . Further, if for any...

Modules de type quasi fini sur un anneau non commutatif

Robert Vidal (1974/1975)

Séminaire Dubreil. Algèbre et théorie des nombres

Modules Graded by G-sets.

C. Nastasescu, F. Van Oystaeyen (1990)

Mathematische Zeitschrift

Modules injectifs indécomposables sur les anneaux artiniens et dualité de Morita

Bernard Roux (1972/1973)

Séminaire Dubreil. Algèbre et théorie des nombres

Modules Over Arbitrary Domains.

Rüdiger Göbel, Saharon Shelah (1984/1985)

Mathematische Zeitschrift

Modules over arbitrary domains II

Rüdiger Göbel, Saharon Shelah (1986)

Fundamenta Mathematicae

Modules over regular algebras of dimension 3.

M. Artin, J. Tate, M. Van den Bergh (1991)

Inventiones mathematicae

Modules over the 4-dimensional Sklyanin algebra

Thierry Levasseur, S.Paul Smith (1993)

Bulletin de la Société Mathématique de France

Modules which are invariant under idempotents of their envelopes

Le Van Thuyet, Phan Dan, Truong Cong Quynh (2016)

Colloquium Mathematicae

We study the class of modules which are invariant under idempotents of their envelopes. We say that a module M is -idempotent-invariant if there exists an -envelope u : M → X such that for any idempotent g ∈ End(X) there exists an endomorphism f : M → M such that uf = gu. The properties of this class of modules are discussed. We prove that M is -idempotent-invariant if and only if for every decomposition $X = ⨁_{i \in I} X_{i}$ , we have $M = ⨁_{i \in I} (u^{- 1} (X_{i}) \cap M)$ . Moreover, some generalizations of -idempotent-invariant modules are considered....

Moduli space of filtered $λ$ -ring structures over a filtered ring.

Yau, Donald (2004)

International Journal of Mathematics and Mathematical Sciences

Monomorphisms of coalgebras

A. L. Agore (2010)

Colloquium Mathematicae

We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, φ: C → D is a monomorphism of coalgebras if and only if the first cohomology groups of the coalgebras C and D coincide if and only if $\sum_{i \in I} ε (a^{i}) b^{i} = \sum_{i \in I} a^{i} ε (b^{i})$ for all $\sum_{i \in I} a^{i} \otimes b^{i} \in C ◻_{D} C$ . In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given.

More examples of invariance under twisting

Florin Panaite (2012)

Czechoslovak Mathematical Journal

The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are particular...

More on the Schur group of a commutative ring.

Mollin, R.A. (1985)

International Journal of Mathematics and Mathematical Sciences

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