The probability that the multiplication of two ring elements is zero
2018 ◽
Vol 17
(03)
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pp. 1850054
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Let [Formula: see text] be a finite commutative ring. We denote by [Formula: see text] the probability that the multiplication of two randomly chosen elements of [Formula: see text] is zero. In this paper, we show that either [Formula: see text] or [Formula: see text] for any ring [Formula: see text] and determine all rings [Formula: see text] with [Formula: see text]. Also, we obtain the structures of rings [Formula: see text] having maximum or minimum value of [Formula: see text] among all rings with identity of the same size. We characterize all rings [Formula: see text] with identity such that [Formula: see text]. Finally, we compute [Formula: see text] where [Formula: see text] is a PIR local ring.
2019 ◽
Vol 12
(04)
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pp. 1950057
Keyword(s):
2017 ◽
Vol 96
(3)
◽
pp. 389-397
2020 ◽
Vol 12
(03)
◽
pp. 2050023
Keyword(s):
2019 ◽
Vol 19
(12)
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pp. 2050226
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Keyword(s):
1965 ◽
Vol 25
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pp. 113-120
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Keyword(s):
2019 ◽
Vol 19
(09)
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pp. 2050173
2005 ◽
Vol 72
(2)
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pp. 317-324
Keyword(s):
2015 ◽
Vol 14
(10)
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pp. 1550107
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Keyword(s):