Strong Cleanness of Matrix Rings Over Commutative Rings

REFERENCES

• Azumaya , G. ( 1951 ). On maximally central algebras . Nagoya J. Math. 2 : 119 – 150 .
   Google Scholar
• Bondarko , M. V. ( 2002 ). The Krull–Schmidt theorem for Henselian rings . J. Math. Sci. 112 , No. 3 .
   Google Scholar
• Burgess , W. D. , Menal , P. ( 1988 ). On strongly π-regular rings and homomorphism into them . Comm. Algebra 18 ( 8 ): 1701 – 1725 .
   Google Scholar
• Chen , J. , Yang , X. , Zhou , Y. ( 2006 ). When is the 2 × 2 matrix ring over a commutative local ring strongly clean? J. Algebra 301 : 280 – 293 .
   Web of Science ®Google Scholar
• Couchot , F. ( 2007 ). Indecomposable modules and Gelfand rings . Comm. Algebra 35 ( 1 ): 231 – 241 .
   Web of Science ®Google Scholar
• Dischinger , F. ( 1976 ). Sur les anneaux fortement π-réguliers . C. R. Acad. Sc. Paris 283 : 571 – 573 .
   Google Scholar
• Fuchs , L. , Salce , L. ( 2001 ). Modules Over Non-Noetherian Domains . Number 84 in Mathematical Surveys and Monographs . Providence : American Mathematical Society .
   Google Scholar
• Han , J. , Nicholson , W. K. (2001). Extensions of clean rings. Comm. Algebra 29:2589–2595.
   Web of Science ®Google Scholar
• Nagata , M. ( 1962 ). Local Rings . New York and London : Intersciences Publishers .
   Google Scholar
• Nicholson , W. K. ( 1977 ). Lifting idempotents and exchange rings . Trans. Amer. Path. Soc. 229 : 269 – 278 .
   Web of Science ®Google Scholar
• Raynaud , M. ( 1970 ). Anneaux Locaux Henséliens . Vol. 169 of Lecture Notes in Mathematics . Berlin-Heidelberg-New York : Springer-Verlag .
   Google Scholar
• Wang , Z. , Chen , J. ( 2004 ). On two problems about strongly clean rings . Bull. Austral. Math. Soc. 70 : 279 – 282 .
   Web of Science ®Google Scholar
• Communicated by R. Wisbauer.
   Google Scholar