Gelfand-Kirillov dimension under base field extension

1991 ◽  
Vol 73 (3) ◽  
pp. 289-296
Author(s):  
Quanshui Wu
Keyword(s):  
Field Extension ◽  
Base Field ◽  
Kirillov Dimension

A REMARK ON GENERIC TAMENESS PRESERVATION UNDER BASE FIELD EXTENSION

2013 ◽  
Vol 12 (04) ◽  
pp. 1250183 ◽  
Author(s):  
GILBERTO MÉNDEZ ◽  
EFRÉN PÉREZ
Keyword(s):  
Algebraic Closure ◽  
Field Extension ◽  
Base Field ◽  
Perfect Field ◽  
Finite Dimensional

Let k be a perfect field, K its algebraic closure and let Λ be a finite-dimensional k-algebra. A result of Kasjan asserts that if k is infinite and Λ is generically tame then Λ ⊗k K is generically tame. We show that the infiniteness requirement can be removed.

scholarly journals MODULES OVER QUANTUM LAURENT POLYNOMIALS

2011 ◽  
Vol 91 (3) ◽  
pp. 323-341 ◽  
Author(s):  
ASHISH GUPTA
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Laurent Polynomials ◽  
Base Field ◽  
Simple Modules ◽  
Holonomic Modules ◽  
Kirillov Dimension

AbstractWe show that the Gelfand–Kirillov dimension for modules over quantum Laurent polynomials is additive with respect to tensor products over the base field. We determine the Brookes–Groves invariant associated with a tensor product of modules. We study strongly holonomic modules and show that there are nonholonomic simple modules.

ON SEMIGENERIC TAMENESS AND BASE FIELD EXTENSION

2015 ◽  
Vol 58 (1) ◽  
pp. 39-53 ◽  
Author(s):  
EFRÉN PÉREZ
Keyword(s):  
Algebraic Closure ◽  
Field Extension ◽  
Base Field ◽  
Perfect Field ◽  
Finite Dimensional ◽  
Finite Dimensional Algebras

AbstractThe notions of central endolength and semigeneric tameness are introduced, and their behaviour under base field extension for finite-dimensional algebras over perfect fields are analysed. Forka perfect field,Kan algebraic closure and Λ a finite-dimensionalk-algebra, here there is a proof that Λ is semigenerically tame if and only if Λ ⊗kKis tame.

scholarly journals Generalizations of the normal basis theorem

2004 ◽  
Vol 94 (2) ◽  
pp. 185 ◽  
Author(s):  
Elise Björkholdt ◽  
Patrik Lundström
Keyword(s):  
Primitive Element ◽  
Galois Field ◽  
Field Extension ◽  
Normal Basis ◽  
Base Field ◽  
Fixed Element ◽  
Basis Theorem

We give several generalizations of the normal basis and primitive element theorems for a finite Galois field extension, with an infinite base field. These generalizations are obtained by considering polynomial expressions of conjugates of a fixed element.

scholarly journals A census of zeta functions of quartic K surfaces over

2016 ◽  
Vol 19 (A) ◽  
pp. 1-11
Author(s):  
Kiran S. Kedlaya ◽  
Andrew V. Sutherland
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Field Extension ◽  
Base Field ◽  
Numerical Evidence ◽  
Recent Theorem ◽  
Complete Set ◽  
Quartic Surfaces

We compute the complete set of candidates for the zeta function of a K$3$surface over$\mathbb{F}_{2}$consistent with the Weil and Tate conjectures, as well as the complete set of zeta functions of smooth quartic surfaces over$\mathbb{F}_{2}$. These sets differ substantially, but we do identify natural subsets which coincide. This gives some numerical evidence towards a Honda–Tate theorem for transcendental zeta functions of K$3$surfaces; such a result would refine a recent theorem of Taelman, in which one must allow an uncontrolled base field extension.

Faktor-Faktor yang Berhubungan dengan Kinerja Penyuluh Pertanian di Kabupaten Ciamis Jawa Barat

2020 ◽  
Vol 4 (4) ◽  
pp. 545
Author(s):  
Nur Puti Kurniawati ◽  
Dwi Sadono ◽  
Endang Sri Wahyuni
Keyword(s):  
Achievement Motivation ◽  
Census Data ◽  
Work Motivation ◽  
Agricultural Extension ◽  
Field Extension ◽  
Need For Achievement ◽  
Extension Agent ◽  
Spearman Correlation Test ◽  
And Performance ◽  
The Relationship

Agricultural extension agent was the main spearhead in carrying out counseling. A good agricultural extension agent can be reflected in their performance. The purpose of this study were: (1) describe the characteristics of agricultural extension agent, (2) describe the level of competence, level of work motivation, and describe level of performance of agricultural extension agent, (3) analyze the relationship between characteristics of agricultural extention agent and the level of performance of agricultural extension agent, (4) analyze the relationship between the level of competency of agricultural extension agent and the level of performance of agricultural extension agent, (5) analyze the relationship between the level of motivation of agricultural extension agent and the level of performance of agricultural extension agent. Responden in this study were 48 field extension agent who are civil servant in Ciamis Regency West Java and selected by census. Data were analyzed using Rank Spearman correlation test. The results showed that agricultural extension agent in Ciamis Regency were dominated by extension agent who were old, undergraduate educated, had little training, and had a long working period. Agricultural extension agent in Ciamis Regency generally have sufficient competency which tends to be high and generally dominated by the need for achievement motivation. The results also show that there is a relationship between managerial competence and performance, social competence with performance, technical competence with performance, level of competency with performance, and the need for achievement with performance.Keywords: Agricultural Extension Agent,Competence, Motivation, Performance.

scholarly journals Normal Bases on Galois Ring Extensions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng
Keyword(s):  
Signal Processing ◽  
Finite Field ◽  
Block Cipher ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Galois Rings ◽  
Ring Extension ◽  
Galois Fields ◽  
Normal Bases

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

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