Title : ( Some remarks on generalizations of the reverse order law in a *-ring )
Authors: hamideh rahmani , Seyyed Alireza Kamel Mirmostafaee ,
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Abstract
We show that if (1 − a†a)b is left *-cancelable, then the reverse order laws (ab)† = b†a† and (ab)† = (abb†a†ab)† are equivalent. By investigating the reverse order law (abb†a†a)♯ = b(abb†a†ab)† in rings with involution, we will show that under certain circumstances the inclusion (abb†a†a){5} ⊆ b(abb†a†ab){1,3,4} is always an equality. MSC 2020. Primary 47A05; Secondary 15A09, 16U90. Key words. Group inverse, Moore-Penrose inverse, left *-cancelable, EP element, idempotent element, reverse order law.
Keywords
, Key words. Group inverse, Moore-Penrose inverse, left *-cancelable, EP element, idempotent element, reverse order law.
@article{paperid:1101605,
author = {Rahmani, Hamideh and Kamel Mirmostafaee, Seyyed Alireza},
title = {Some remarks on generalizations of the reverse order law in a *-ring},
journal = {Mathematica},
year = {2024},
volume = {66 (89)},
number = {2},
month = {December},
issn = {1222-9016},
pages = {262--277},
numpages = {15},
keywords = {Key words. Group inverse; Moore-Penrose inverse; left *-cancelable; EP element; idempotent element; reverse order law.},
}
%0 Journal Article
%T Some remarks on generalizations of the reverse order law in a *-ring
%A Rahmani, Hamideh
%A Kamel Mirmostafaee, Seyyed Alireza
%J Mathematica
%@ 1222-9016
%D 2024
