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Considering the ring of integers in a number field as a $Z Γ$ -module (where $Γ$ is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.

Some examples of nil Lie algebras

Ivan P. Shestakov, Efim Zelmanov (2008)

Journal of the European Mathematical Society

Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.

Some external characterizations of SV-rings and hereditary rings.

Haily, A., Rahnaoui, H. (2007)

International Journal of Mathematics and Mathematical Sciences

Some remarks on global dimensions for cotorsion pairs

Edgar E. Enochs, Hae-Sik Kim (2006)

Rendiconti del Seminario Matematico della Università di Padova

Some remarks on the Akivis algebras and the Pre-Lie algebras

Yuqun Chen, Yu Li (2011)

Czechoslovak Mathematical Journal

In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I. P. Shestakov’s result that any Akivis algebra is linear and D. Segal’s result that the set of all good words in $X^{* *}$ forms a linear basis of the free Pre-Lie algebra $PLie (X)$ generated by the set $X$ . For completeness,...

Some torsion theoretical characterizations of rings.

Ahsan, Javed (1984)

International Journal of Mathematics and Mathematical Sciences

Spectrum of the quantized Weyl algebra. (Spectre de l'algèbre de Weyl quantique.)

Rigal, Laurent (1996)

Beiträge zur Algebra und Geometrie

Spinors in braided geometry

Mićo Đurđević, Zbigniew Oziewicz (1996)

Banach Center Publications

Let V be a ℂ-space, $σ \in E n d (V^{\otimes 2})$ be a pre-braid operator and let $F \in l i n (V^{\otimes 2}, ℂ) .$ This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra $C l (V, σ, 0) \equiv V^{\land} (σ)$ . If $σ \neq σ^{- 1}$ and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...

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