A. R. Wadsworth's Publications

  1. Pairs of domains where all intermediate domains are Noetherian. Trans. Amer. Math. Soc. 195 (1974), 201--211. (MR 50#2158)

  2. Similarity of quadratic forms and isomorphism of their function fields. Trans. Amer. Math. Soc. 208 (1975), 352--358. (MR 51#12702)

  3. Hilbert subalgebras of finitely generated algebras. J. Algebra 43 (1976), no. 1, 298--304. (MR 55#329)

  4. (with Daniel Shapiro) Spaces of similarities. III. Function fields. J. Algebra 46 (1977), no. 1, 182--188. (MR 56#11898c)

  5. Hilbert subalgebras of finitely generated algebras. II. Comm. Algebra 5 (1977), no. 8, 863--872. (MR 56#3002)

  6. (with Daniel Shapiro) On multiples of round and Pfister forms. Math. Z. 157 (1977), no. 1, 53--62. (MR 58#21938)

  7. (with Richard Elman and T. Y. Lam) Amenable fields and Pfister extensions. Conference on Quadratic Forms---1976 (Proc. Conf., Queen's Univ., Kingston, Ont., 1976), pp. 445--492. With an appendix ``Excellence of $F(\varphi )/F$ for 2-fold Pfister forms'' by J. K. Arason. Queen's Papers in Pure and Appl. Math., No. 46, Queen's Univ., Kingston, Ont., 1977. (MR 58#27756)

  8. (with Richard Elman and T. Y. Lam) Orderings under field extensions. J. Reine Angew. Math. 306 (1979), 7--27. (MR 80e:12029)

  9. (with Richard Resco and Lance Small) Tensor products of division rings and finite generation of subfields. Proc. Amer. Math. Soc. 77 (1979), no. 1, 7--10. (MR 80g:16020)

  10. The Krull dimensions of tensor products of commutative algebras over a field. J. London Math. Soc. (2) 19 (1979), no. 3, 391--401. (MR 80h:13014)

  11. (with Richard Elman and T. Y. Lam) Function fields of Pfister forms. Invent. Math. 51 (1979), no. 1, 61--75. (MR 80m:10017)

  12. Polynomial invariants for operators. Integral Equations Operator Theory 2 (1979), no. 3, 421--433. (MR 81c:47038)

  13. (with Richard Elman and T. Y. Lam) Pfister ideals in Witt rings. Math. Ann. 245 (1979), no. 3, 219--245. (MR 81g:10037)

  14. (with Richard Elman and T. Y. Lam) Quadratic forms under multiquadratic extensions. Nederl. Akad. Wetensch. Indag. Math. 42 (1980), no. 2, 131--145. (MR 81j:10028)

  15. (with Burton Fein and Murray Schacher) Division rings and the square root of $-1$. J. Algebra 65 (1980), no. 2, 340--346. (MR 81j:12015)

  16. (with Lance Small) An example in affine PI-rings. Israel J. Math. 36 (1980), no. 3-4, 285--286. (MR 82a:16022)

  17. (with Lance Small) Some examples of rings. Comm. Algebra 9 (1981), no. 10, 1105--1118. (MR 82h:16012)

  18. $p$-Henselian fields: $K$-theory, Galois cohomology, and graded Witt rings. Pacific J. Math. 105 (1983), no. 2, 473--496. (MR 84m:12026)

  19. (with Richard Elman, T. Y. Lam, and J.-P. Tignol) Witt rings and Brauer groups under multiquadratic extensions. I. Amer. J. Math. 105 (1983), no. 5, 1119--1170. (MR 85i:11032)

  20. (with Daniel Shapiro and J.-P. Tignol) Witt rings and Brauer groups under multiquadratic extensions. II. J. Algebra 78 (1982), no. 1, 58--90. (MR 85i:11033)

  21. (with Lance Small) Integrality of subrings of matrix rings. Pacific J. Math. 116 (1985), no. 1, 195--200. (MR 86i:16017)

  22. Discriminants in characteristic two. Linear and Multilinear Algebra 17 (1985), no. 3-4, 235--263. (MR 86m:12004)

  23. (with Bill Jacob) A new construction of noncrossed product algebras. Trans. Amer. Math. Soc. 293 (1986), no. 2, 693--721. (MR 87g:16027)

  24. (with David Leep and Daniel Shapiro) Sums of squares in division algebras. Math. Z. 190 (1985), no. 2, 151--162. (MR 87i:11047)

  25. Extending valuations to finite-dimensional division algebras. Proc. Amer. Math. Soc. 98 (1986), no. 1, 20--22. (MR 87i:16025)

  26. Merkurjev's elementary proof of Merkurjev's theorem. Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), 741--776, Contemp. Math., 55, Amer. Math. Soc., Providence, R.I., 1986. (MR 88b:11078)

  27. (with J.-P. Tignol) Totally ramified valuations on finite-dimensional division algebras. Trans. Amer. Math. Soc. 302 (1987), no. 1, 223--250. (MR 88j:16025)

  28. (with Richard Elman) Hereditarily quadratically closed fields. J. Algebra 111 (1987), no. 2, 475--482. (MR 89g:12004)

  29. (with David Leep) The transfer ideal of quadratic forms and a Hasse norm theorem mod squares. Trans. Amer. Math. Soc. 315 (1989), no. 1, 415--432. (MR 90a:11047)

  30. The residue division ring of a valued division algebra. Deuxième Contact Franco-Belge en Algèbre (Faulx-les-Tombes, 1987). Bull. Soc. Math. Belg. Sér. A 40 (1988), no. 2, 307--322. (MR 90b:16028)

  31. Dubrovin valuation rings and Henselization. Math. Ann. 283 (1989), no. 2, 301--328. (MR 90f:16009)

  32. (with Patrick Morandi) Baer orderings with noninvariant valuation ring. Israel J. Math. 68 (1989), no. 2, 241--255. (MR 91c:12002)

  33. (with Bill Jacob) Division algebras over Henselian fields. J. Algebra 128 (1990), no. 1, 126--179. (MR 91d:12006)

  34. (with Patrick Morandi) Integral Dubrovin valuation rings. Trans. Amer. Math. Soc. 315 (1989), no. 2, 623--640. (MR 91d:16076)

  35. Dubrovin valuation rings. Perspectives in ring theory (Antwerp, 1987), 359--374, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., 233, Kluwer Acad. Publ., Dordrecht, 1988. (MR 91e:16053)

  36. In a division algebra of even degree $-1$ is a product of squares. Bull. Soc. Math. Belg. Sér. B 42 (1990), no. 1, 103--104. (MR 91h:12007)

  37. The algebra generated by two commuting matrices. Linear and Multilinear Algebra 27 (1990), no. 3, 159--162. (MR 91h:16053b)

  38. (with M. Chacron) On decomposing $c$-valued division rings. J. Algebra 134 (1990), no. 1, 182--208. (MR 91j:16055)

  39. (with P. Mammone and J.-P. Tignol) Fields of characteristic $2$ with prescribed $u$-invariants. Math. Ann. 290 (1991), no. 1, 109--128. (MR 92g:11035)

  40. (with P. Mammone and R. Moresi) $u$-invariants of fields of characteristic $2$. Math. Z. 208 (1991), no. 3, 335--347. (MR 92m:11033)

  41. Valuations on tensor products of symbol algebras. Azumaya algebras, actions, and modules (Bloomington, IN, 1990), 275--289, Amer. Math. Soc., Providence, RI, 1992. (MR 93a:16015)

  42. (with David Leep) The Hasse norm theorem mod squares. J. Number Theory 42 (1992), no. 3, 337--348. (MR 94b:11109)

  43. The index reduction formula for generic partial splitting varieties. Comm. Algebra 21 (1993), no. 4, 1063--1070. (MR 94g:16022)

  44. (with Bill Jacob) Division algebras with no common subfields. Israel J. Math. 83 (1993), no. 3, 353--360. (MR 95a:12005)

  45. (with Krüskemper, Martin) A quaternion algebra of sublevel $3$. Bull. Soc. Math. Belg. Sér. B 43 (1991), no. 2,181--185. (MR 95j:11035)

  46. (with M. Chacron, H. Dherte, and J.-P. Tignol) Yanchevski\u\i, V. I. Discriminants of involutions on Henselian division algebras. Pacific J. Math. 167 (1995), no. 1, 49--79. (MR 95k:16020)

  47. (with Ján Miná\vc, ) The $u$-invariant for algebraic extensions. $K$-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992), 333--358, Proc. Sympos. Pure Math., 58, Part 2, Amer. Math. Soc., Providence, RI, 1995. (MR 96e:11052)

  48. (with Darrell Haile and Patrick Morandi) Bézout orders and Henselization. J. Algebra 173 (1995), no. 2, 394--423. (MR 96i:16025)

  49. Review of "Quadratic algebras, Clifford algebras, and arithmetic Witt groups" by A.J. Hahn (Springer, 1994) in Bull. Amer. Math. Soc. 33 (1996), no. 2, 263--267.

  50. (with A. S. Merkurjev and I. A. Panin) Index reduction formulas for twisted flag varieties, I. K-Theory 10 (1996), 517-596. (MR 98c: 16018)

  51. (with R. S. Garibaldi and J.-P. Tignol) Galois cohomology of special orthogonal groups. Manuscripta Math. 93 (1997), 247-266. (MR 98k: 11039)

  52. (with A. S. Merkurjev and I. A. Panin) Index reduction formulas for twisted flag varieties, II. K-Theory 14 (1998), 101-196. (MR 99k: 16037)

  53. (with Y.-S. Hwang) Algebraic extensions of graded and valued fields, Comm. Algebra 27 (1999) 821-840. (MR 2000d: 12006)

  54. (with M. Chacron and J.-P. Tignol) Tractable fields, Canadian J. Math. 51 (1999) 10-25.  (MR 2000e: 16020)

  55. (with Y.-S. Hwang) Correspondences between valued division algebras and graded division algebras J. Algebra 220 (1999), 73-114. (MR 2000g: 16028)

  56. Valuation theory on finite dimensional division algebras, Fields Institute Communications, 32 (2002), 385-449.  (MR 2003g: 16023)

  57. (with Y.-S. Hwang and D. B. Leep) Galois groups of order 2n that contain a cyclic group of order n, Pacific J. Math., 212 (2003), 297-319. (MR 2004m: 12002)

  58. (with. E. Aljadeff and J. Sonn) Projective Schur groups of Henselian fields, J. Pure Appl. Algebra, 208 (2007), 833-851. (MR 2007k: 11196)

  59. (with J. Minac) Division algebras of prime degree and maximal Galois p-extensions, Canad. J. Math., 59 (2007), 658-672. (MR 2319163)

  60. (with R. Hazrat) Nontriviality of certain quotients of K1 groups of division algebras, J. Algebra, 312 (2007),  354--361. (MR 2320461)

  61. (with J.-F. Renard and J.-P. Tignol) Graded Hermitian forms and Springer's theorem, Indag. Math. (N.S.), 18 (2007), 97--134. (MR 2330736)

  62. (with C. D. Popescu and J. Sonn) n-torsion of Brauer groups as relative Brauer groups of abelian extensions, J. Number Theory, 125 (2007), 26--38.  (MR 2333116)

  63. (with R. Hazrat) On maximal subgroups of the multiplicative group of a division algebra, J. Algebra, 322 (2009), 2528--2543.

  64. (with J.-P. Tignol) Value functions and associated graded rings for semisimple algebras, Trans. Amer. Math. Soc.,  362 (2010), 687--726.

  65. (with K. Mounirh) Subfields of nondegenerate tame semiramified division algebras, Comm. Algebra, 39 (2011),  462–485.

  66. (with R. Hazrat) SK1 of graded division algebras, Israel J. Math., 183 (2011), 117–163.

  67. (with J.-P. Tignol) Valuations on algebras with involution, Math. Ann., 351 (2011), 109–148.

  68. (with V. I. Yanchevskii) Unitary SK1 for a graded division ring and its quotient division ring, J. Algebra, 352 (2012), 62 - 78.

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A. Wadsworth / arwadsworth@ucsd.edu