Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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f-CLEAN RINGS AND RINGS HAVING MANY FULL ELEMENTS

  • Li, Bingjun (Hunan Institute of Humanities Science and Technology) ;
  • Feng, Lianggui (Department of Mathematics and Systems Science, National University of Defense Technology)
  • Published : 2010.03.01
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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 = $\(\array{A\;V\\W\;B}\)$ be 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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References

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