The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules

Oliver W. Gnilke; Marcus Greferath; Thomas Honold; Jay A. Wood; Jens Zumbraegel

doi:10.1090/conm/727/14629

The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules

Oliver W. Gnilke^*
, Marcus Greferath
, Thomas Honold
, Jay A. Wood
, Jens Zumbraegel

^*Corresponding author for this work

University of Passau
Zhejiang University
Western Michigan University

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

5 Citations (Web of Science)

231 Downloads (Pure)

Abstract

We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the complex monoid algebra of the multiplicative monoid of the coefficient ring.

Original language	English
Title of host publication	Rings, Modules and Codes
Editors	A Leroy, C Lomp, S LopezPermouth, F Oggier
Publisher	American Mathematical Society
Pages	117-129
Number of pages	13
ISBN (Electronic)	978-1-4704-5237-7
ISBN (Print)	978-1-4704-4104-3
DOIs	https://doi.org/10.1090/conm/727/14629
Publication status	Published - 2019
MoE publication type	A4 Conference publication
Event	International Conference on Noncommutative Rings and their Applications - Lens, France Duration: 12 Jun 2017 → 15 Jun 2017 Conference number: 5

Publication series

Name	Contemporary Mathematics
Publisher	AMER MATHEMATICAL SOC
Volume	727
ISSN (Print)	0271-4132

Conference

Conference	International Conference on Noncommutative Rings and their Applications
Country/Territory	France
City	Lens
Period	12/06/2017 → 15/06/2017

Keywords

FINITE
MODULES
CODES
EQUIVALENCE

Access to Document

10.1090/conm/727/14629

SCI_Gnilke_Greferath_et.al_The_Extension_Theorem.paperAccepted author manuscript, 211 KB

Cite this

Gnilke, O. W., Greferath, M., Honold, T., Wood, J. A., & Zumbraegel, J. (2019). The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules. In A. Leroy, C. Lomp, S. LopezPermouth, & F. Oggier (Eds.), Rings, Modules and Codes (pp. 117-129). (Contemporary Mathematics; Vol. 727). American Mathematical Society. https://doi.org/10.1090/conm/727/14629

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title = "The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules",

abstract = "We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the complex monoid algebra of the multiplicative monoid of the coefficient ring.",

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author = "Gnilke, \{Oliver W.\} and Marcus Greferath and Thomas Honold and Wood, \{Jay A.\} and Jens Zumbraegel",

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series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

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editor = "A Leroy and C Lomp and S LopezPermouth and F Oggier",

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note = "International Conference on Noncommutative Rings and their Applications ; Conference date: 12-06-2017 Through 15-06-2017",

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Gnilke, OW, Greferath, M, Honold, T, Wood, JA & Zumbraegel, J 2019, The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules. in A Leroy, C Lomp, S LopezPermouth & F Oggier (eds), Rings, Modules and Codes. Contemporary Mathematics, vol. 727, American Mathematical Society, pp. 117-129, International Conference on Noncommutative Rings and their Applications, Lens, France, 12/06/2017. https://doi.org/10.1090/conm/727/14629

The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules. / Gnilke, Oliver W.; Greferath, Marcus; Honold, Thomas et al.
Rings, Modules and Codes. ed. / A Leroy; C Lomp; S LopezPermouth; F Oggier. American Mathematical Society, 2019. p. 117-129 (Contemporary Mathematics; Vol. 727).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules

AU - Gnilke, Oliver W.

AU - Greferath, Marcus

AU - Honold, Thomas

AU - Wood, Jay A.

AU - Zumbraegel, Jens

N1 - Conference code: 5

PY - 2019

Y1 - 2019

N2 - We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the complex monoid algebra of the multiplicative monoid of the coefficient ring.

AB - We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the complex monoid algebra of the multiplicative monoid of the coefficient ring.

KW - FINITE

KW - MODULES

KW - CODES

KW - EQUIVALENCE

U2 - 10.1090/conm/727/14629

DO - 10.1090/conm/727/14629

M3 - Conference article in proceedings

SN - 978-1-4704-4104-3

T3 - Contemporary Mathematics

SP - 117

EP - 129

BT - Rings, Modules and Codes

A2 - Leroy, A

A2 - Lomp, C

A2 - LopezPermouth, S

A2 - Oggier, F

PB - American Mathematical Society

T2 - International Conference on Noncommutative Rings and their Applications

Y2 - 12 June 2017 through 15 June 2017

ER -

The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules

Abstract

Publication series

Conference

Keywords

Access to Document

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Cite this