Idealiser rings of injective dimension one

AW Chatters

doi:10.1142/S1005386706000228

Idealiser rings of injective dimension one

AW Chatters

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We study a certain type of prime Noetherian idealiser ring R of injective dimension 1, and prove for instance that the idempotent ideals of R are projective and that every non-zero projective ideal of R is uniquely of the form U E for some invertible ideal U and idempotent ideal E of R. Formulae are given for the number of idempotent ideals of R and the number of orders which contain R.

Translated title of the contribution	Idealiser rings of injective dimension one
Original language	English
Pages (from-to)	239 - 252
Number of pages	14
Journal	Algebra Colloquium
Volume	13 (2)
DOIs	https://doi.org/10.1142/S1005386706000228
Publication status	Published - Jun 2006

Bibliographical note

Publisher: World Scientific

Access to Document

10.1142/S1005386706000228

http://www.worldscinet.com/ac/13/1302/S1005386706000228.html

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title = "Idealiser rings of injective dimension one",

abstract = "We study a certain type of prime Noetherian idealiser ring R of injective dimension 1, and prove for instance that the idempotent ideals of R are projective and that every non-zero projective ideal of R is uniquely of the form U E for some invertible ideal U and idempotent ideal E of R. Formulae are given for the number of idempotent ideals of R and the number of orders which contain R.",

author = "AW Chatters",

note = "Publisher: World Scientific",

year = "2006",

month = jun,

doi = "10.1142/S1005386706000228",

language = "English",

volume = "13 (2)",

pages = "239 -- 252",

journal = "Algebra Colloquium",

issn = "1005-3867",

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T1 - Idealiser rings of injective dimension one

AU - Chatters, AW

N1 - Publisher: World Scientific

PY - 2006/6

Y1 - 2006/6

N2 - We study a certain type of prime Noetherian idealiser ring R of injective dimension 1, and prove for instance that the idempotent ideals of R are projective and that every non-zero projective ideal of R is uniquely of the form U E for some invertible ideal U and idempotent ideal E of R. Formulae are given for the number of idempotent ideals of R and the number of orders which contain R.

AB - We study a certain type of prime Noetherian idealiser ring R of injective dimension 1, and prove for instance that the idempotent ideals of R are projective and that every non-zero projective ideal of R is uniquely of the form U E for some invertible ideal U and idempotent ideal E of R. Formulae are given for the number of idempotent ideals of R and the number of orders which contain R.

U2 - 10.1142/S1005386706000228

DO - 10.1142/S1005386706000228

M3 - Article (Academic Journal)

VL - 13 (2)

SP - 239

EP - 252

JO - Algebra Colloquium

JF - Algebra Colloquium

SN - 1005-3867

ER -