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- Title
ON A SPECIAL CLASS OF EXACT SEQUENCES.
- Authors
LÜ, JIA-FENG; CHEN, MIAO-SEN; Trlifaj, J.
- Abstract
The notion of good exact sequence is introduced, which is a special class of exact sequences including split exact sequences as special examples. Several criteria characterizing good exact sequences are given. In particular, we prove that the exact sequence ξ: 0 → K → M → N → 0 is good if and only if the Horseshoe Lemma is true in the "minimal version" with respect to ξ. We also give a lot of nontrivial examples of good exact sequences via "Koszul" objects. Moreover, some applications of good exact sequences are also provided in the end.
- Subjects
MATHEMATICAL sequences; PROJECTIVE spaces; FREE resolutions (Algebra); NUMERICAL analysis; MATHEMATICAL analysis; MATHEMATICAL proofs
- Publication
Journal of Algebra & Its Applications, 2011, Vol 10, Issue 5, p915
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S021949881100504X