Extending partial orders on rings

被引：1

作者：

Findler, Moreta ^{[1
]}

Ma, Jingjing ^{[1
]}

机构：

[1] Univ Houston Clear Lake, Dept Math & Stat, 2700 Bay Area Blvd, Houston, TX 77058 USA

来源：

QUAESTIONES MATHEMATICAE | 2021年 / 44卷 / 07期

关键词：

Primary; Consistently L*-ring; consistently O*-ring; left division closed; L*-ring; O*-ring;

D O I：

10.2989/16073606.2020.1752841

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a commutative ring with identity, it is consistently L* if and only if it is consistently O*. This result is generalized to noncommutative rings with identity in the section 2. In the section 3, it is shown that for any abelian group G and integral domain D, the group ring D[G] is L* if and only if it is O*.

引用

页码：869 / 879

页数：11

共 50 条

[1] Extending partial orders to dense linear orders
Slaman, TA
Woodin, WH
ANNALS OF PURE AND APPLIED LOGIC, 1998, 94 (1-3) : 253 - 261
[2] PARTIAL ORDERS ON *-REGULAR RINGS
Kudaybergenov, K. K.
Nurjanov, B. O.
UFA MATHEMATICAL JOURNAL, 2023, 15 (01): : 34 - 42
[3] On partial orders in Rickart rings
Marovt, Janko
LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (09): : 1707 - 1723
[4] ON PARTIAL ORDERS IN PROPER *-RINGS
Marovt, Janko
REVISTA DE LA UNION MATEMATICA ARGENTINA, 2018, 59 (01): : 193 - 204
[5] On lattice extensions of partial orders of rings
Wojciechowski, PJ
Kreinovich, V
COMMUNICATIONS IN ALGEBRA, 1997, 25 (03) : 935 - 941
[6] PARTIAL ORDERS ON A FIELD AND VALUATION RINGS
BECKER, E
COMMUNICATIONS IN ALGEBRA, 1979, 7 (18) : 1933 - 1976
[7] Extending Orders on Rings with Idempotents and d-elements
Jingjing Ma
R. H. Redfield
Order, 2022, 39 : 309 - 322
[8] Extending Orders on Rings with Idempotents and d-elements
Ma, Jingjing
Redfield, R. H.
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2022, 39 (02): : 309 - 322
[9] EXTENDING PARTIAL RIGHT ORDERS ON NILPOTENT GROUPS
FORMANEK, E
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1973, 7 (AUG): : 131 - 134
[10] On some generalized inverses and partial orders in *-rings
Marovt, Janko
Mosic, Dijana
Cremer, Insa
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (12)

← 1 2 3 4 5 →