<i>n</i>-Clean Rings and Weakly Unit Stable Range Rings

Xiao, Gao; Tong, Wenting

doi:10.1081/agb-200060531

Cited by 22 publications

(20 citation statements)

References 14 publications

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“…are both n -clean [4]. (iii) Let n be a positive integer and suppose that e is a central idempotent of R .…”

Section: Corner Rings Of Clean and Related Ringsmentioning

confidence: 99%

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Some properties of clean rings and their generalisations

Chin¹,

Qua²

2013

AIP Conference Proceedings

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Let R be an associative ring with identity. An element x R is clean if x can be written as the sum of an idempotent element and a unit in R . The ring R is said to be clean if all of its elements are clean. An element x R is weakly clean if x can be written as x u e or x u e for some unit u and idempotent e in R . The ring R is said to be weakly clean if all of its elements are weakly clean. Let n be a positive integer. An element x R is n -clean if x can be written as the sum of an idempotent and n units in R . The ring R is said to be n -clean if all of its elements are n -clean. In this paper we extend some results on clean rings to weakly clean rings and n -clean rings.

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“…are both n -clean [4]. (iii) Let n be a positive integer and suppose that e is a central idempotent of R .…”

Section: Corner Rings Of Clean and Related Ringsmentioning

confidence: 99%

“…(iii) Let n be a positive integer and suppose that e is a central idempotent of R . If R is an n -clean, then so is Re e [4]. (iv) An element Re e a is strongly clean in R if and only if a is strongly clean in Re e [5].…”

Section: Corner Rings Of Clean and Related Ringsmentioning

confidence: 99%

Some properties of clean rings and their generalisations

Chin¹,

Qua²

2013

AIP Conference Proceedings

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“…For n -weakly clean rings, we obtain the following: It is known that homomorphic images of n -clean rings are n -clean (see [1]). For n -weakly clean rings we have the following: PROPOSITION 4.…”

Section: Propositionmentioning

confidence: 99%

“…The ring R is said to be n -clean if all of its elements are n -clean. This notion of n -cleanness first appeared in [1]. Following [2], an element x R is said to be weakly clean if or x u e x u e for some unit u and idempotent e in R .…”

Section: Introductionmentioning

confidence: 99%

Some properties of n-weakly clean rings

Chin¹,

Qua²

2014

AIP Conference Proceedings

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“…Semiperfect rings and unit-regular rings are examples of clean rings as shown by Camillo and Yu [5] and Camillo and Khurana [4]. In recent years, many authors have studied clean rings and their generalizations such as [1,13,16,17].…”

Section: Introductionmentioning

confidence: 99%

f-CLEAN RINGS AND RINGS HAVING MANY FULL ELEMENTS

Li¹,

Feng²

2010

Journal of the Korean Mathematical Society

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Abstract. An associative ring R with identity is called a clean ring if every element of R is the sum of a unit and an idempotent. In this paper, we introduce the concept of f -clean rings. We study various properties of f -clean rings. Let C =`A V W B´b e a Morita Context ring. We determine conditions under which the ring C is f -clean. Moreover, we introduce the concept of rings having many full elements. We investigate characterizations of this kind of rings and show that rings having many full elements are closed under matrix rings and Morita Context rings.

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n-Clean Rings and Weakly Unit Stable Range Rings

Cited by 22 publications

References 14 publications

Some properties of clean rings and their generalisations

Some properties of clean rings and their generalisations

Some properties of n-weakly clean rings

f-CLEAN RINGS AND RINGS HAVING MANY FULL ELEMENTS

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