Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets

Sophie Frisch

Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets

Institute of Analysis and Number Theory (5010)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

Regarding polynomial functions on a subset S of a non-commutative
ring R, that is, functions induced by polynomials in R[x] (whose variable commutes with the coeffcients), we show connections between, on one hand, sets S such that the integer-valued polynomials on S form a ring, and, on the other hand, sets S such that the set of polynomials in R[x] that are zero on S is an ideal of R[x].

Original language	English
Title of host publication	Proceedings of the international confreence on mathematics Dec 18-22, 2018, at Ton Duc Thang University (TDTU)
Publisher	EDP Sciences
Number of pages	8
Publication status	Published - 18 Dec 2018
Event	International Conference on Mathematics 2018, Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics - Ton Duc Thang University (TDTU), Ho Chi Minh City, Viet Nam Duration: 18 Dec 2018 → 20 Dec 2018 https://icm2018.tdtu.edu.vn/ http://icm2018.tdtu.edu.vn/

Publication series

Name	ITM Web of Conferences
Publisher	EDP Sciences
Number	18
Volume	2018
ISSN (Electronic)	2271-2097

Conference

Conference	International Conference on Mathematics 2018, Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
Country/Territory	Viet Nam
City	Ho Chi Minh City
Period	18/12/18 → 20/12/18
Internet address	https://icm2018.tdtu.edu.vn/ http://icm2018.tdtu.edu.vn/

Keywords

rings, modules, algebras
non-commutative rings
polynomial functions
polynomial mappings
matrix algebras
null polynomials
ring sets
null-ideal sets
null ideals
finite rings

ASJC Scopus subject areas

Algebra and Number Theory

Fields of Expertise

Information, Communication & Computing

Access to Document

https://doi.org/10.1051/itmconf/20182001003

Cite this

Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets. / Frisch, Sophie.
Proceedings of the international confreence on mathematics Dec 18-22, 2018, at Ton Duc Thang University (TDTU). EDP Sciences, 2018. (ITM Web of Conferences; Vol. 2018, No. 18).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Frisch, S 2018, Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets. in Proceedings of the international confreence on mathematics Dec 18-22, 2018, at Ton Duc Thang University (TDTU). ITM Web of Conferences, no. 18, vol. 2018, EDP Sciences, International Conference on Mathematics 2018, Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics, Ho Chi Minh City, Viet Nam, 18/12/18. <https://doi.org/10.1051/itmconf/20182001003>

@inproceedings{0590cfefb0d94f5ebb1f155d9e01dba1,

title = "Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets",

abstract = "Regarding polynomial functions on a subset S of a non-commutativering R, that is, functions induced by polynomials in R[x] (whose variable commutes with the coeffcients), we show connections between, on one hand, sets S such that the integer-valued polynomials on S form a ring, and, on the other hand, sets S such that the set of polynomials in R[x] that are zero on S is an ideal of R[x].",

keywords = "rings, modules, algebras, non-commutative rings, polynomial functions, polynomial mappings, matrix algebras, null polynomials, ring sets, null-ideal sets, null ideals, finite rings",

author = "Sophie Frisch",

year = "2018",

month = dec,

day = "18",

language = "English",

series = "ITM Web of Conferences",

publisher = "EDP Sciences",

number = "18",

booktitle = "Proceedings of the international confreence on mathematics Dec 18-22, 2018, at Ton Duc Thang University (TDTU)",

address = "France",

note = "International Conference on Mathematics 2018, Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics ; Conference date: 18-12-2018 Through 20-12-2018",

url = "https://icm2018.tdtu.edu.vn/, http://icm2018.tdtu.edu.vn/",

}

TY - GEN

T1 - Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets

AU - Frisch, Sophie

PY - 2018/12/18

Y1 - 2018/12/18

N2 - Regarding polynomial functions on a subset S of a non-commutativering R, that is, functions induced by polynomials in R[x] (whose variable commutes with the coeffcients), we show connections between, on one hand, sets S such that the integer-valued polynomials on S form a ring, and, on the other hand, sets S such that the set of polynomials in R[x] that are zero on S is an ideal of R[x].

AB - Regarding polynomial functions on a subset S of a non-commutativering R, that is, functions induced by polynomials in R[x] (whose variable commutes with the coeffcients), we show connections between, on one hand, sets S such that the integer-valued polynomials on S form a ring, and, on the other hand, sets S such that the set of polynomials in R[x] that are zero on S is an ideal of R[x].

KW - rings, modules, algebras

KW - non-commutative rings

KW - polynomial functions

KW - polynomial mappings

KW - matrix algebras

KW - null polynomials

KW - ring sets

KW - null-ideal sets

KW - null ideals

KW - finite rings

UR - https://www.itm-conferences.org/articles/itmconf/abs/2018/05/contents/contents.html

UR - http://blah.math.tu-graz.ac.at/~frisch/wwwpdf/ring-and-nullideal-sets__S._Frisch.pdf

M3 - Conference paper

T3 - ITM Web of Conferences

BT - Proceedings of the international confreence on mathematics Dec 18-22, 2018, at Ton Duc Thang University (TDTU)

PB - EDP Sciences

T2 - International Conference on Mathematics 2018, Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics

Y2 - 18 December 2018 through 20 December 2018

ER -

Polynomial functions on subsets of non-commutative rings — a link between ringsets and null-ideal sets

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

Other files and links

Fingerprint

Cite this