Generators of maximal orders

Rostyslav Kravchenko; Marcin Mazur; Bogdan V. Petrenko

doi:10.1016/j.jalgebra.2014.11.020

Generators of maximal orders

Rostyslav Kravchenko, Marcin Mazur^*, Bogdan V. Petrenko

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let R be the ring of algebraic integers in a number field K and let Λ be a maximal order in a finite dimensional semisimple K-algebra B. Building on our previous work [3], we compute the smallest number of algebra generators of Λ considered as an R-algebra. This reproves and vastly extends the results of P.A.B. Pleasants, who considered the case when B is a number field. In order to achieve our goal, we obtain several results about counting generators of algebras which have finitely many elements. These results should be of independent interest.

Original language	English (US)
Pages (from-to)	32-50
Number of pages	19
Journal	Journal of Algebra
Volume	426
DOIs	https://doi.org/10.1016/j.jalgebra.2014.11.020
State	Published - Mar 5 2015

Keywords

Generators of algebras
Maximal orders
Smallest number of generators

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2014.11.020

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title = "Generators of maximal orders",

abstract = "Let R be the ring of algebraic integers in a number field K and let Λ be a maximal order in a finite dimensional semisimple K-algebra B. Building on our previous work [3], we compute the smallest number of algebra generators of Λ considered as an R-algebra. This reproves and vastly extends the results of P.A.B. Pleasants, who considered the case when B is a number field. In order to achieve our goal, we obtain several results about counting generators of algebras which have finitely many elements. These results should be of independent interest.",

keywords = "Generators of algebras, Maximal orders, Smallest number of generators",

author = "Rostyslav Kravchenko and Marcin Mazur and Petrenko, {Bogdan V.}",

note = "Funding Information: This work was partially supported by a grant from the Simons Foundation (# 245855 to Marcin Mazur). Publisher Copyright: {\textcopyright} 2014 Elsevier Inc..",

year = "2015",

month = mar,

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doi = "10.1016/j.jalgebra.2014.11.020",

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TY - JOUR

T1 - Generators of maximal orders

AU - Kravchenko, Rostyslav

AU - Mazur, Marcin

AU - Petrenko, Bogdan V.

PY - 2015/3/5

Y1 - 2015/3/5

N2 - Let R be the ring of algebraic integers in a number field K and let Λ be a maximal order in a finite dimensional semisimple K-algebra B. Building on our previous work [3], we compute the smallest number of algebra generators of Λ considered as an R-algebra. This reproves and vastly extends the results of P.A.B. Pleasants, who considered the case when B is a number field. In order to achieve our goal, we obtain several results about counting generators of algebras which have finitely many elements. These results should be of independent interest.

AB - Let R be the ring of algebraic integers in a number field K and let Λ be a maximal order in a finite dimensional semisimple K-algebra B. Building on our previous work [3], we compute the smallest number of algebra generators of Λ considered as an R-algebra. This reproves and vastly extends the results of P.A.B. Pleasants, who considered the case when B is a number field. In order to achieve our goal, we obtain several results about counting generators of algebras which have finitely many elements. These results should be of independent interest.

KW - Generators of algebras

KW - Maximal orders

KW - Smallest number of generators

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DO - 10.1016/j.jalgebra.2014.11.020

M3 - Article

AN - SCOPUS:84920097667

SN - 0021-8693

VL - 426

SP - 32

EP - 50

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Generators of maximal orders

Abstract

Keywords

ASJC Scopus subject areas

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