Unique factorization in polynomial rings with zero divisors
2020 ◽
pp. 2150113
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Keyword(s):
Given a certain factorization property of a ring [Formula: see text], we can ask if this property extends to the polynomial ring over [Formula: see text] or vice versa. For example, it is well known that [Formula: see text] is a unique factorization domain if and only if [Formula: see text] is a unique factorization domain. If [Formula: see text] is not a domain, this is no longer true. In this paper, we survey unique factorization in commutative rings with zero divisors, and characterize when a polynomial ring over an arbitrary commutative ring has unique factorization.
1979 ◽
Vol 28
(4)
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pp. 423-426
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1969 ◽
Vol 65
(3)
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pp. 579-583
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1992 ◽
Vol 53
(3)
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pp. 287-293
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2018 ◽
Vol 17
(07)
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pp. 1850121
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2012 ◽
Vol 55
(1)
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pp. 127-137
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1991 ◽
Vol 109
(2)
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pp. 287-297
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2020 ◽
Vol 12
(1)
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pp. 84-101
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