Notes on Pointfree Disconnectivity with a Ring-theoretic Slant

被引：24

作者：

Dube, Themba ^{[1
]}

机构：

[1] Univ S Africa, Dept Math Sci, ZA-0003 Unisa, South Africa

来源：

APPLIED CATEGORICAL STRUCTURES | 2010年 / 18卷 / 01期

关键词：

Frame; F-frame; Basically disconnected; Extremally disconnected; Ring of continuous functions on a frame; Ring-ideal; Large compactification; F-RINGS;

D O I：

10.1007/s10485-008-9162-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give characterizations of extremally disconnected frames, basically disconnected frames and F-frames L in terms of ring-theoretic properties of the ring RL of continuous real-valued functions on L. Emanating from these are new (and purely ring-theoretic) proofs that a frame is extremally disconnected, basically disconnected or an F-frame iff the same holds for its Cech-Stone compactification.

引用

页码：55 / 72

页数：18

共 50 条

[1] Notes on Pointfree Disconnectivity with a Ring-theoretic Slant
Themba Dube
Applied Categorical Structures, 2010, 18 : 55 - 72
[2] General Ring-Theoretic Results
Abrams, Gene
Ara, Pere
Siles Molina, Mercedes
LEAVITT PATH ALGEBRAS, 2017, 2191 : 151 - 184
[3] Ring-theoretic properties of PvMDs
El Baghdadi, Said
Gabelli, Stefania
COMMUNICATIONS IN ALGEBRA, 2007, 35 (05) : 1607 - 1625
[4] Ring-theoretic blowing down. I
Rogalski, Daniel
Sierra, Susan J.
Stafford, J. Toby
JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2017, 11 (04) : 1465 - 1520
[5] RING-THEORETIC PROPERTIES OF CERTAIN HECKE ALGEBRAS
TAYLOR, R
WILES, A
ANNALS OF MATHEMATICS, 1995, 141 (03) : 553 - 572
[6] Some ring-theoretic properties of group algebras
Dong, XD
Soh, CB
Gunawan, E
COMMUNICATIONS IN ALGEBRA, 1999, 27 (05) : 2117 - 2126
[7] Ring-theoretic properties of commutative algebras of invariants
Kantor, I
Rowen, LH
JOURNAL OF ALGEBRA, 2003, 266 (01) : 239 - 260
[8] Ring-theoretic foundation of convolutional network coding
Li, Shuo-Yen Robert
Ho, Siu Ting
2008 FOURTH WORKSHOP ON NETWORK CODING, THEORY, AND APPLICATIONS: NETCOD 2008, PROCEEDINGS, 2008, : 56 - 61
[9] Explicit ring-theoretic presentation of Iwasawa algebras
Ray, Jishnu
COMPTES RENDUS MATHEMATIQUE, 2018, 356 (11-12) : 1075 - 1080
[10] More ring-theoretic characterizations of P-frames
Dube, Themba
Ighedo, Oghenetega
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (05)

← 1 2 3 4 5 →