On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic

Alberto F. Boix; Danny A.J. Gómez–Ramírez; Santiago Zarzuela

doi:10.1007/s40306-023-00515-3

On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic

Alberto F. Boix, Danny A.J. Gómez–Ramírez, Santiago Zarzuela

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

Abstract

Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is to study in some detail when (Formula presented.) is an open set in the Zariski topology, where FE^p denotes the Frobenius algebra attached to the injective hull of the residue field of R_p. We show that this is true when R is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.

Original language	English
Pages (from-to)	3-18
Number of pages	16
Journal	Acta Mathematica Vietnamica
Volume	49
Issue number	1
DOIs	https://doi.org/10.1007/s40306-023-00515-3
State	Published - 1 Mar 2024
Externally published	Yes

Keywords

13A35
13F55
Frobenius algebras
Stanley–Reisner rings

ASJC Scopus subject areas

General Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1007/s40306-023-00515-3

Cite this

@article{ab79dcc7e7c244f286ba49829e35afd0,

title = "On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic",

abstract = "Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is to study in some detail when (Formula presented.) is an open set in the Zariski topology, where FEp denotes the Frobenius algebra attached to the injective hull of the residue field of Rp. We show that this is true when R is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.",

keywords = "13A35, 13F55, Frobenius algebras, Stanley–Reisner rings",

author = "Boix, {Alberto F.} and G{\'o}mez–Ram{\'i}rez, {Danny A.J.} and Santiago Zarzuela",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2023.",

year = "2024",

month = mar,

day = "1",

doi = "10.1007/s40306-023-00515-3",

language = "English",

volume = "49",

pages = "3--18",

journal = "Acta Mathematica Vietnamica",

issn = "0251-4184",

publisher = "Springer Verlag",

number = "1",

}

TY - JOUR

T1 - On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic

AU - Boix, Alberto F.

AU - Gómez–Ramírez, Danny A.J.

AU - Zarzuela, Santiago

N1 - Publisher Copyright: © Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2023.

PY - 2024/3/1

Y1 - 2024/3/1

N2 - Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is to study in some detail when (Formula presented.) is an open set in the Zariski topology, where FEp denotes the Frobenius algebra attached to the injective hull of the residue field of Rp. We show that this is true when R is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.

AB - Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is to study in some detail when (Formula presented.) is an open set in the Zariski topology, where FEp denotes the Frobenius algebra attached to the injective hull of the residue field of Rp. We show that this is true when R is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.

KW - 13A35

KW - 13F55

KW - Frobenius algebras

KW - Stanley–Reisner rings

UR - http://www.scopus.com/inward/record.url?scp=85178492321&partnerID=8YFLogxK

U2 - 10.1007/s40306-023-00515-3

DO - 10.1007/s40306-023-00515-3

M3 - Article

AN - SCOPUS:85178492321

SN - 0251-4184

VL - 49

SP - 3

EP - 18

JO - Acta Mathematica Vietnamica

JF - Acta Mathematica Vietnamica

IS - 1

ER -

On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this