Further results on the reverse order law for the Moore–Penrose inverse in rings with involution

2011 ◽  
Vol 218 (4) ◽  
pp. 1478-1483 ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution

Weighted Reverse Order Law for the Weighted Moore-Penrose Inverse in Rings with Involution

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution ◽  
Necessary And Sufficient

Abstract We investigate some necessary and sufficient conditions for the reverse order law for the weighted Moore-Penrose inverse in rings with involution.

scholarly journals Core partial order in rings with involution

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5695-5701 ◽  
Author(s):  
Xiaoxiang Zhang ◽  
Sanzhang Xu ◽  
Jianlong Chen
Keyword(s):  
Partial Order ◽  
Partial Orders ◽  
Reverse Order ◽  
Unital Ring ◽  
Reverse Order Law ◽  
Rings With Involution ◽  
Invertible Elements

Let R be a unital ring with involution. Several characterizations and properties of core partial order in R are given. In particular, we investigate the reverse order law (ab)# = b#a# for two core invertible elements a, b ? R. Some relationships between core partial order and other partial orders are obtained.

scholarly journals Reverse order law (ab)+ = b+(a+abb+)+a+ in rings with involution

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1791-1815 ◽  
Author(s):  
Dijana Mosic ◽  
Nebojsa Dincic
Keyword(s):  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution ◽  
Equivalent Conditions

In this paperwestudy several equivalent conditions for the reverse order law (ab)+ = b+(a+abb+)+a+ in rings with involution. We extend some well-known results to more general settings.

Some results on the reverse order law in rings with involution

2012 ◽  
Vol 83 (3) ◽  
pp. 271-282 ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution

scholarly journals Mixed-type reverse order law for Moore-Penrose inverse of products of three elements in ring with involution

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 1997-2008 ◽  
Author(s):  
Long Wang ◽  
Shuang Zhang ◽  
Xiao Zhang ◽  
Jian Chen
Keyword(s):  
Mixed Type ◽  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution

In this paper we establish some results concerning the mixed-type reverse order laws for the Moore-Penrose inverse of various products of three elements in rings with involution.

scholarly journals Generalizations of the reverse order law with related results

1974 ◽  
Vol 8 (4) ◽  
pp. 345-349 ◽  
Author(s):  
David T. Barwick ◽  
Jimmie D. Gilbert
Keyword(s):  
Reverse Order ◽  
Reverse Order Law
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