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ON SEPARATIVE REFINEMENT MONOIDS

  • Chen, Huanyin (DEPARTMENT OF MATHEMATICS HANGZHOU NORMAL UNIVERSITY)
  • Published : 2009.05.31

Abstract

We obtain two new characterizations of separativity of refinement monoids, in terms of comparability-type conditions. As applications, we get several equivalent conditions of separativity for exchange ideals.

Keywords

References

  1. P. Ara, Extensions of exchange rings, J. Algebra 197 (1997), no. 2, 409–423 https://doi.org/10.1006/jabr.1997.7116
  2. P. Ara, Stability properties of exchange rings, International Symposium on Ring Theory (Kyongju, 1999), 23–42, Trends Math., Birkhauser Boston, Boston, MA, 2001
  3. P. Ara, K. R. Goodearl, K. C. O'Meara, and E. Pardo, Separative cancellation for projective modules over exchange rings, Israel J. Math. 105 (1998), 105–137 https://doi.org/10.1007/BF02780325
  4. G. Brookfield, Monoids and Categories of Noetherian Modules, Ph. D. Thesis, University of California, 1997
  5. K. R. Goodearl, Von Neumann Regular Rings, Monographs and Studies in Mathematics, 4. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979
  6. K. R. Goodearl, Von Neumann regular rings and direct sum decomposition problems, Abelian groups and modules (Padova, 1994), 249–255, Math. Appl., 343, Kluwer Acad. Publ., Dordrecht, 1995
  7. E. Pardo, Comparability, separativity, and exchange rings, Comm. Algebra 24 (1996), no. 9, 2915–2929 https://doi.org/10.1080/00927879608825721
  8. F. Wehrung, Restricted injectivity, transfer property and decompositions of separative positively ordered monoids, Comm. Algebra 22 (1994), no. 5, 1747–1781 https://doi.org/10.1080/00927879408824934

Cited by

  1. Tame and wild refinement monoids vol.91, pp.1, 2015, https://doi.org/10.1007/s00233-014-9647-3