Polycyclic-by-finite group algebras are catenary

被引：0

作者：

Letzter, ES ^{[1
]}

Lorenz, M

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

来源：

MATHEMATICAL RESEARCH LETTERS | 1999年 / 6卷 / 02期

关键词：

group algebra; polycyclic-by-finite group; prime ideal; catenary ring; noetherian ring; second layer condition;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that group algebras kG of polycyclic-by-finite groups G, where k is a field, are catenary: If P = I-0 not subset of or equal to I-1 not subset of or equal to ... not subset of or equal to I-m = P' and P = J(0) not subset of or equal to J(2) not subset of or equal to ... not subset of or equal to J(n) = P' are both saturated chains of prime ideals of kG, then m = n.not subset of or equal to

引用

页码：183 / 194

页数：12

共 50 条

[21] Semiprime CS group algebra of polycyclic-by-finite group without domains as summands is hereditary
Alahmadi, Adel N.
Jain, S. K.
Srivastava, J. B.
JOURNAL OF ALGEBRA, 2007, 307 (02) : 541 - 546
[22] THE ALGORITHMIC THEORY OF POLYCYCLIC-BY-FINITE GROUPS
BAUMSLAG, G
CANNONITO, FB
ROBINSON, DJS
SEGAL, D
JOURNAL OF ALGEBRA, 1991, 142 (01) : 118 - 149
[23] Homotopy dominations by polyhedra with polycyclic-by-finite fundamental groups
Kolodziejczyk, D
TOPOLOGY AND ITS APPLICATIONS, 2005, 153 (2-3) : 294 - 302
[24] ANALOGS OF CLIFFORD THEOREM FOR POLYCYCLIC-BY-FINITE GROUPS
LORENZ, M
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 254 (OCT) : 295 - 317
[25] Groups with polycyclic-by-finite conjugate classes of subgroups
Kurdachenko, LA
Otal, J
Soules, P
COMMUNICATIONS IN ALGEBRA, 2004, 32 (12) : 4769 - 4784
[26] SOLVABLE LIE-ALGEBRAS POLYCYCLIC-BY-FINITE GROUPS AND BI-MODULE KRULL DIMENSION
JATEGAONKAR, AV
COMMUNICATIONS IN ALGEBRA, 1982, 10 (01) : 19 - 69
[27] SPLITTING GROUPS OVER POLYCYCLIC-BY-FINITE SUBGROUPS
DUNWOODY, MJ
ROLLER, MA
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1993, 25 : 29 - 36
[28] Hypercentrally embedded subgroups of polycyclic-by-finite groups
Maier, Rudolf
JOURNAL OF GROUP THEORY, 2012, 15 (06) : 785 - 791
[29] DIVISORIALLY GRADED RINGS BY POLYCYCLIC-BY-FINITE GROUPS
MARUBAYASHI, H
COMMUNICATIONS IN ALGEBRA, 1989, 17 (09) : 2135 - 2177
[30] Derivations and the permutability of subgroups in polycyclic-by-finite groups
Robinson, DJS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (12) : 3461 - 3464

← 1 2 3 4 5 →