# Reverse Order Law for the Core Inverse in Rings

Reverse Order Law for the Core Inverse in Rings In this paper, necessary and sufficient conditions of the one-sided reverse order law $$(ab)^{\tiny {\textcircled {\tiny \#}}}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # a # , the two-sided reverse order law $$(ab)^{\tiny {\textcircled {\tiny \#}}}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # a # and $$(ba)^{\tiny {\textcircled {\tiny \#}}}=a^{\tiny {\textcircled {\tiny \#}}}b^{\tiny {\textcircled {\tiny \#}}}$$ ( b a ) # = a # b # for the core inverse are given in rings with involution. In addition, the mixed-type reverse order laws, such as $$(ab)^{\#}=b^{\tiny {\textcircled {\tiny \#}}}(abb^{\tiny {\textcircled {\tiny \#}}})^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # ( a b b # ) # , $$a^{\tiny {\textcircled {\tiny \#}}}=b(ab)^{\#}$$ a # = b ( a b ) # and $$(ab)^{\#}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # a # , are also considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# Reverse Order Law for the Core Inverse in Rings

, Volume 15 (3) – Jun 5, 2018
17 pages

/lp/springer_journal/reverse-order-law-for-the-core-inverse-in-rings-0WOC5c0lyl
Publisher
Springer International Publishing
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-018-1189-6
Publisher site
See Article on Publisher Site

### Abstract

In this paper, necessary and sufficient conditions of the one-sided reverse order law $$(ab)^{\tiny {\textcircled {\tiny \#}}}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # a # , the two-sided reverse order law $$(ab)^{\tiny {\textcircled {\tiny \#}}}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # a # and $$(ba)^{\tiny {\textcircled {\tiny \#}}}=a^{\tiny {\textcircled {\tiny \#}}}b^{\tiny {\textcircled {\tiny \#}}}$$ ( b a ) # = a # b # for the core inverse are given in rings with involution. In addition, the mixed-type reverse order laws, such as $$(ab)^{\#}=b^{\tiny {\textcircled {\tiny \#}}}(abb^{\tiny {\textcircled {\tiny \#}}})^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # ( a b b # ) # , $$a^{\tiny {\textcircled {\tiny \#}}}=b(ab)^{\#}$$ a # = b ( a b ) # and $$(ab)^{\#}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$ ( a b ) # = b # a # , are also considered.

### Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jun 5, 2018

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