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

Guédénon, Thomas (2003)

Beiträge zur Algebra und Geometrie

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Guédénon, Thomas (2003)

Beiträge zur Algebra und Geometrie

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Guédénon, Thomas (2004)

Beiträge zur Algebra und Geometrie

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Gupta, Vishnu, Chaudhari, J.N. (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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Ferrero, Miguel, Steffenon, Rogério Ricardo (2004)

Beiträge zur Algebra und Geometrie

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K. Samei (2000)

Colloquium Mathematicae

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The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).

Rtveliashvili, E. (1996)

Georgian Mathematical Journal

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Chandan Singh Dalawat (2009)

Journal de Théorie des Nombres de Bordeaux

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We show how K. Hensel could have extended Wilson’s theorem from $\mathbf{Z}$ to the ring of integers $\U0001d52c$ in a number field, to find the product of all invertible elements of a finite quotient of $\U0001d52c$.

Debremaeker, R., van Lierde, V. (2006)

Beiträge zur Algebra und Geometrie

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Chaopraknoi, Sureeporn, Savettaseranee, Knograt, Lertwichitsilp, Patcharee (2005)

General Mathematics

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Ali, Majid M. (2007)

Beiträge zur Algebra und Geometrie

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Denis Simon (2008)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we study equations of the form $C{y}^{d}=F(x,z)$, where $F\in \mathbb{Z}[x,z]$ is a binary form, homogeneous of degree $n$, which is supposed to be primitive and irreducible, and $d$ is any fixed integer. Using classical tools in algebraic number theory, we prove that the existence of a proper solution for this equation implies the existence of an integral ideal of given norm in some order in a number field, and also the existence of a specific relation in the class group involving this ideal. In some cases,...