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ON THE FALSITY OF EULER'S CONJECTURE ABOUT THE NON-EXISTENCE OF TWO ORTHOGONAL LATIN SQUARES OF ORDER 4t + 2.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bose, R. C. Shrikhande, S. S. |
| Copyright Year | 1959 |
| Abstract | y in (q2 n ... n q) -p we have that (xj): y = p. Since x; is not in Up and hd p < 1, it follows from the previous proposition that p = (xj). THEOREM 3. Let R be a local domain of dimension 1 and dim R < 3. Thus hd R/p < 2, which completes the proof. Since every module has finite homological dimension over a regular local ring, we have established COROLLARY 4. Every regular local ring of dimension <3 is a unique factorization domain. THEOREM 5. Every regular local ring is a unique factorization domain. |
| File Format | PDF HTM / HTML |
| DOI | 10.1073/pnas.45.5.734 |
| Alternate Webpage(s) | http://www.stat.ncsu.edu/information/library/mimeo.archive/ISMS_1959_220.pdf |
| Alternate Webpage(s) | http://www.pnas.org/content/45/5/734.full.pdf |
| Alternate Webpage(s) | http://www.stat.ncsu.edu/library/mimeo.archive/ISMS_1959_220.pdf |
| PubMed reference number | 16590435 |
| Alternate Webpage(s) | https://doi.org/10.1073/pnas.45.5.734 |
| Journal | Medline |
| Volume Number | 45 |
| Issue Number | 5 |
| Journal | Proceedings of the National Academy of Sciences of the United States of America |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |