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• W66408083 abstract "AbstractWe establish commutativity theorems for certain classes of rings in which every invertible element is central, or, more generally, in which all invertible elements commute with one another. We prove that if R is a semiexchange ring (i.e., its factor ring modulo its Jacobson radical is an exchange ring) with all invertible elements central, then R is commutative. We also prove that if R is a semiexchange ring in which all invertible elements commute with one another, and R has no factor ring with two elements, then R is commutative. We offer some examples of noncommutative rings in which all invertible elements commute with one another, or are central. We close with a list of problems for further research.Mathematics Subject Classification (2000)Primary 16U6016U70Secondary16L30KeywordsUnit-centralrings with commuting unitsexchange ringssemiexchange ringscommutativity theorems" @default.
• W66408083 created "2016-06-24" @default.
• W66408083 creator A5012954356 @default.
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• W66408083 date "2010-01-01" @default.
• W66408083 modified "2023-09-27" @default.
• W66408083 title "On Unit-Central Rings" @default.
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• W66408083 doi "https://doi.org/10.1007/978-3-0346-0286-0_13" @default.
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