Planar ternary ring (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Planar ternary ring" in English language version.

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Hall 1943 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
Hughes & Piper 1973, p. 113, Thm. 5.1. Hughes, Daniel R.; Piper, Fred C. (1973), Projective Planes, Graduate Texts in Mathematics (6), New York: Springer-Verlag, ISBN 0387900446, MR 0333959
Hughes & Piper 1973, p. 118, Theorem 5.4 Hughes, Daniel R.; Piper, Fred C. (1973), Projective Planes, Graduate Texts in Mathematics (6), New York: Springer-Verlag, ISBN 0387900446, MR 0333959
In the literature there are two versions of this definition. This is the form used by Hall (1959, p. 355), Albert & Sandler (1968, p. 50), and Dembowski (1968, p. 128), while $a\oplus b=T(1,a,b)$ is used by Hughes & Piper (1973, p. 117), Pickert (1975, p. 38), and Stevenson (1972, p. 274). The difference comes from the alternative ways these authors coordinatize the plane. Hall, Marshall Jr. (1959), The Theory of Groups, New York: The MacMillan Company, MR 0103215 Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275 Hughes, Daniel R.; Piper, Fred C. (1973), Projective Planes, Graduate Texts in Mathematics (6), New York: Springer-Verlag, ISBN 0387900446, MR 0333959 Pickert, Günter (1975), Projektive Ebenen, Berlin: Springer-Verlag, ISBN 3540072802 Stevenson, Frederick (1972), Projective Planes, San Francisco: W.H. Freeman and Company, ISBN 071670443-9
Hall 1943, p.247 Theorem 5.4 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
This can be done in several ways. A short description of the method used by Hall (1943) can be found in Dembowski (1968, p. 127). Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link) Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275
Dembowski 1968, p. 129 Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275

archive.org

In the literature there are two versions of this definition. This is the form used by Hall (1959, p. 355), Albert & Sandler (1968, p. 50), and Dembowski (1968, p. 128), while $a\oplus b=T(1,a,b)$ is used by Hughes & Piper (1973, p. 117), Pickert (1975, p. 38), and Stevenson (1972, p. 274). The difference comes from the alternative ways these authors coordinatize the plane. Hall, Marshall Jr. (1959), The Theory of Groups, New York: The MacMillan Company, MR 0103215 Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275 Hughes, Daniel R.; Piper, Fred C. (1973), Projective Planes, Graduate Texts in Mathematics (6), New York: Springer-Verlag, ISBN 0387900446, MR 0333959 Pickert, Günter (1975), Projektive Ebenen, Berlin: Springer-Verlag, ISBN 3540072802 Stevenson, Frederick (1972), Projective Planes, San Francisco: W.H. Freeman and Company, ISBN 071670443-9
This can be done in several ways. A short description of the method used by Hall (1943) can be found in Dembowski (1968, p. 127). Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link) Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275
Dembowski 1968, p. 129 Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275

doi.org

Hall 1943 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
Hall 1943, p.247 Theorem 5.4 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
This can be done in several ways. A short description of the method used by Hall (1943) can be found in Dembowski (1968, p. 127). Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link) Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275

jstor.org

Hall 1943 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
Hall 1943, p.247 Theorem 5.4 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
This can be done in several ways. A short description of the method used by Hall (1943) can be found in Dembowski (1968, p. 127). Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link) Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275

worldcat.org

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Hall 1943 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
Hall 1943, p.247 Theorem 5.4 Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link)
This can be done in several ways. A short description of the method used by Hall (1943) can be found in Dembowski (1968, p. 127). Hall, Marshall, Jr. (1943), "Projective planes", Transactions of the American Mathematical Society, 54 (2), American Mathematical Society: 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892{{citation}}: CS1 maint: multiple names: authors list (link) Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275