Rings in which every left zero-divisor is also a right zero-divisor and conversely
2019 ◽
Vol 18
(05)
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pp. 1950096
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Keyword(s):
A ring [Formula: see text] is called eversible if every left zero-divisor in [Formula: see text] is also a right zero-divisor and conversely. This class of rings is a natural generalization of reversible rings. It is shown that every eversible ring is directly finite, and a von Neumann regular ring is directly finite if and only if it is eversible. We give several examples of some important classes of rings (such as local, abelian) that are not eversible. We prove that [Formula: see text] is eversible if and only if its upper triangular matrix ring [Formula: see text] is eversible, and if [Formula: see text] is eversible then [Formula: see text] is eversible.
2019 ◽
Vol 19
(03)
◽
pp. 2050053
2016 ◽
Vol 15
(07)
◽
pp. 1650121
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2009 ◽
Vol 51
(3)
◽
pp. 425-440
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Keyword(s):
2004 ◽
Vol 70
(2)
◽
pp. 279-282
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