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Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.

The Exterior Derivation and the Orders of Differential Forms on Contractible Algebras.

Shuzo Izumi (1979)

Mathematische Annalen

The Extraordinary Derived Category.

Alan Robinson (1987)

Mathematische Zeitschrift

The finite dimension property of the irreducible representations of Noetherian $p$ -Lie algebras.

Shevelin, M.A. (2004)

Sibirskij Matematicheskij Zhurnal

The flat dimensions of injective modules.

Nanqing Ding, Jianlong Chen (1993)

Manuscripta mathematica

The free $A$ -ring is a graded $A$ -ring.

Warren, Roger D. (1993)

International Journal of Mathematics and Mathematical Sciences

The Frobenius theorem on $N$ -dimensional quantum hyperplane.

Ciupală, C. (2006)

Acta Mathematica Universitatis Comenianae. New Series

The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules

Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2016)

Colloquium Mathematicae

We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category $̃ (ℳ_{k})$ . More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.

The $G$ -graded identities of the Grassmann Algebra

Lucio Centrone (2016)

Archivum Mathematicum

Let $G$ be a finite abelian group with identity element $1_{G}$ and $L = ⨁_{g \in G} L^{g}$ be an infinite dimensional $G$ -homogeneous vector space over a field of characteristic $0$ . Let $E = E (L)$ be the Grassmann algebra generated by $L$ . It follows that $E$ is a $G$ -graded algebra. Let $| G |$ be odd, then we prove that in order to describe any ideal of $G$ -graded identities of $E$ it is sufficient to deal with $G^{'}$ -grading, where $| G^{'} | \leq | G |$ , ${dim}_{F} L^{1_{G^{'}}} = \infty$ and ${dim}_{F} L^{g^{'}} < \infty$ if $g^{'} \neq 1_{G^{'}}$ . In the same spirit of the case $| G |$ odd, if $| G |$ is even it is sufficient to study only those $G$ -gradings such that...

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The elliptic $GL (n)$ dynamical quantum group as an $𝔥$ -Hopf algebroid.

The Endomorphism Ring Theorem for Frobenius Extensions.

The Equivalence of Various Generalizations of Group Rings and Modules.

The existence of envelopes

The existence of Galois sets

The existence of identity of orthodox semigroup rings.

The existence of relative pure injective envelopes

The Exterior Derivation and the Orders of Differential Forms on Contractible Algebras.

The Extraordinary Derived Category.

The finite dimension property of the irreducible representations of Noetherian $p$ -Lie algebras.

The flat dimensions of injective modules.

The free $A$ -ring is a graded $A$ -ring.

The Frobenius theorem on $N$ -dimensional quantum hyperplane.

The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules

The $G$ -graded identities of the Grassmann Algebra

The Galois algebras and the Azumaya Galois extensions.

The Galois extensions induced by idempotents in a Galois algebra.

The Galois module structure of algebraic integer rings in fields with generalised quaternion group

The Gelfand-Kirillov Dimension of a Tensor Product.

The Gelfand-Kirillov dimension of rings with Hopf algebra action.

Currently displaying 81 – 100 of 290