### Certain near-rings are rings. II.

Bell, Howard E. (1986)

International Journal of Mathematics and Mathematical Sciences

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Bell, Howard E. (1986)

International Journal of Mathematics and Mathematical Sciences

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Alessandra Cherubini, Ada Varisco (1988)

Czechoslovak Mathematical Journal

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Huanyin Chen (2008)

Czechoslovak Mathematical Journal

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Let $R$ be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in $R$ is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.

Heatherly, H.E., Courville, J.R. (1999)

Mathematica Pannonica

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Kaplansky, Irving (1951)

Portugaliae mathematica

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Mohamed A. Salim, Adela Tripe (2011)

Czechoslovak Mathematical Journal

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In this paper, we extend some results of D. Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power ${2}^{{\aleph}_{0}}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.

Huanyin Chen, Fu-An Li (2002)

Collectanea Mathematica

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In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.