π-COMPLEMENTATION IN THE UNITISATION AND MULTIPLICATION ALGEBRAS OF A SEMIPRIME ALGEBRA

被引：2
|
作者：
Cabello, J. C. [1 ]
Cabrera, M. [1 ]
Roura, R. [1 ]
机构：
[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain
来源：
COMMUNICATIONS IN ALGEBRA | 2012年 / 40卷 / 09期
关键词：
Central closure; Complemented algebra; Extended centroid; Multiplication algebra; Semiprime algebra; CENTRAL CLOSURE;
D O I：
10.1080/00927872.2011.590954
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
pi-complemented algebras are defined as those (not necessarily associative or unital) algebras such that each annihilator ideal is complemented by other annihilator ideal. For a given semiprime algebra A, we discuss the pi-complementation of the unitisation algebra A(1) of A. Moreover, if in addition the multiplication algebra M(A) of A is also semiprime, we study the pi-complementation in the algebras M(A) and M-#(A) (the multiplication ideal of A). In associative setting, we prove that A is pi-complemented if and only if M-#(A) is pi-complemented, and that A(1) pi-complemented if and only if M(A) is pi-complemented.
引用
收藏
页码：3507 / 3531
页数：25
相关论文
共 50 条
  • [1] Closed prime ideals in algebras with semiprime multiplication algebra
    Cabello, J. C.
    Cabrera, M.
    Nieto, E.
    COMMUNICATIONS IN ALGEBRA, 2007, 35 (12) : 4245 - 4276
  • [2] Algebras whose multiplication algebra is semiprime. A decomposition theorem
    Cabello, J. C.
    Cabrera, M.
    JOURNAL OF ALGEBRA, 2008, 319 (03) : 911 - 937
  • [3] Algebras of quotients with bounded evaluation of a normed semiprime algebra
    Cabrera, M
    Mohammed, AA
    STUDIA MATHEMATICA, 2003, 154 (02) : 113 - 135
  • [4] The multiplication algebra of weighted algebras of degree 4
    Costa, R
    Suazo, A
    COMMUNICATIONS IN ALGEBRA, 2002, 30 (11) : 5345 - 5357
  • [5] Algebras whose multiplication algebra is PI or GPI
    Cabrera, M.
    Fernandez Lopez, A.
    Golubkov, A. Yu
    Moreno, A.
    JOURNAL OF ALGEBRA, 2016, 459 : 213 - 237
  • [6] Semiprime Novikov algebras
    Panasenko, A. S.
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2022, 32 (07) : 1369 - 1378
  • [7] SEMIPRIME BANACH ALGEBRAS
    DIXON, PG
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1973, 6 (24): : 676 - 678
  • [8] θ-Centralizers on Semiprime Banach *-algebras
    I. Nikoufar
    Th. M. Rassias
    Ukrainian Mathematical Journal, 2014, 66 : 300 - 310
  • [9] SEMIPRIME SUBMODULES OF GRADED MULTIPLICATION MODULES
    Lee, Sang Cheol
    Varmazyar, Rezvan
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 49 (02) : 435 - 447
  • [10] θ-Centralizers on Semiprime Banach *-algebras
    Nikoufar, I.
    Rassias, Th. M.
    UKRAINIAN MATHEMATICAL JOURNAL, 2014, 66 (02) : 300 - 310
12345