Publications of Lindsay N. Childs

Mathematical Publications

Books

• A Concrete Introduction to Higher Algebra, Springer-Verlag, New York (Undergraduate Texts in Mathematics series) 1979; Second Edition, 1995; second corrected printing, 1997; first softcover printing, 2000.
• Algebra, un'introduzione concreta, (translation of the First Edition by Carlo Traverso), ETS Editrice Pisa, 1989.
• Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, American Mathematical Society, Mathematical Surveys and Monographs, vol. 80, 2000.

Professional Publications

1. On automorphisms of separable algebras (with F. R. DeMeyer), Pacific J. Math. 23 (1967), 25-34.
2. A note on the fixed ring of a Galois extension, Osaka J. Math 4 (1967), 173-175.
3. On projective modules and automorphisms of central separable algebras, Canadian J. Math. 21 (1969), 44-53.
4. The exact sequence of low degree and normal algebras, Bull. Amer. Math. Soc. 76 (1970), 1121-1124.
5. Abelian Galois extensions of rings containing roots of unity, Illinois J. Math. 15 (1971), 273-280.
6. On covering spaces and Galois extensions, Pacific J. Math. 37 (1971), 29-33.
7. On normal Azumaya algebras and the Teichmuller cocycle map, J. Algebra 23 (1972), 1-17.
8. The Brauer group of graded Azumaya algebras (with G. Garfinkel and M. Orzech), Trans. Amer. Math. Soc. 175 (1973), 299-326.
9. Mayer-Vietoris sequences and Brauer groups of non-normal domains, Trans. Amer. Math. Soc. 196 (1974), 51-67.
10. Brauer groups of affine rings, in Ring Theory, Proceedings of the Oklahoma Conference, Marcel Dekker, 1974, 83-93.
11. The Picard invariant of principal homogeneous spaces (with A. Magid), J. Pure Appl. Algebra 4 (1974), 273-286.
12. The Brauer group of graded Azumaya algebras II: graded Galois extensions, Trans. Amer. Math. Soc. 204 (1975), 137- 160.
13. On the Brauer group and factoriality of normal domains (with G. Garfinkel and M. Orzech), J. Pure Appl. Algebra 6 (1975), 111-123.
14. The full Brauer group and Cech cohomology, Chapter 13 of The Brauer Group of Commutative Rings, by M. Orzech and C. Small, Pure and Applied Mathematics Series, Vol. 11, Marcel Dekker, 1975, 147-162.
15. On the group of Galois extensions of prime degree, Proc. Conf. on Commutative Algebra, Queen's Lecture Notes on Pure and Applied Math. 42 (1975), 242-248.
16. On Brauer groups of some normal local rings, Brauer Groups, Evanston, 1975, Springer Lecture Notes in Math. 549 (1976), 1-15.
17. The group of unramified Kummer extensions of prime degree, Proc. London Math. Soc. 35 (1977), 407-422.
18. Linearizing of n-ic forms and generalized Clifford algebras, Linear and Multilinear Algebra 5 (1978), 267-278.
19. Stickelberger relations on tame Kummer extensions of prime degree, Proc. Conference on Number Theory, Queen's Papers in Pure and Applied Math. 54 (1980), 249-256.
20. Stickelberger relations and tame extensions of prime degree, Illinois J. Math 25 (1981), 258-266.
21. On modular group rings, normal bases and fixed points (with M. Orzech), American Mathematical Monthly 88 (1981), 142-145.
22. A Stickelberger condition on cyclic Galois extensions, Canadian J. Math. 34 (1982), 686-690.
23. Tame Kummer extensions and Stickelberger conditions, Illinois J. Math. 28 (1984), 547-554.
24. Cyclic Stickelberger cohomology and descent of Kummer extensions, Proc. Amer. Math. Soc. 90 (1984), 505-510.
25. Tameness and local normal bases for objects of finite Hopf algebras (with S. Hurley), Trans. Amer. Math. Soc. 298 (1986), 763-778.
26. Products of Galois objects and the Picard invariant map, Math J. Okayama Univ.28 (1986) 29-36. .
27. Representing classes in the Brauer group of quadratic number rings as smash products, Pacific J. Math. 129 (1987), 243-255.
28. Taming wild extensions with Hopf algebras, Trans. Amer. Math. Soc. 304 (1987), 111-140.
29. Non-isomorphic equivalent Azumaya algebras, Canadian Math. Bull. 30 (1987), 340-343.
30. On Hopf Galois extensions of fields and number rings, in Perspectives in Ring Theory, F. van Oystaeyen and L. LeBruyn eds., Kluwer, 1988, 117-1128.
31. On the Hopf Galois theory for separable field extensions, Comm. Algebra 17 (1989), 809-825.
32. Azumaya algebras which are not smash products, Rocky Mountain J. Math. 20 (1990), 75-89.
33. Congruence-torsion subgroups of dimension one formal groups (with Karl Zimmermann), J. Algebra 170 (1994), 929- 955.
34. Hopf algebras and local Galois module theory (with David Moss), in Advances in Hopf Algebras (J. Bergen and S. Montgomery, eds.) Marcel Dekker, 1994, 1-24.
35. Galois extensions over local number rings, in Rings, Extensions and Homology, (A. Magid, ed.), Marcel Dekker, 1994, 41-66.
36. Hopf Galois structures on degree p^2 extensions of local fields, New York J. Math. 2 (1996), 86-102.
37. Introduction to polynomial formal groups and Hopf algebras, Memoirs Amer. Math. Soc. vol. 136, No. 651 (1998), 1-10.
38. Dimension one polynomial formal groups (with D. Moss, J. Sauerberg), Memoirs Amer. Math. Soc. vol. 136, No. 651 (1998), 11-20.
39. Dimension two polynomial formal groups and Hopf algebras (with D. Moss, J. Sauerberg, K. Zimmermann), Memoirs Amer. Math. Soc. vol. 136, No. 651 (1998), 21-54.
40. Degree 2 formal groups and Hopf algebras (with J. Sauerberg), Memoirs Amer. Math. Soc. vol. 136, No. 651 (1998), 55-90.
41. p-elementary group schemes--construction, and Raynaud's theory (with C. Greither), Memoirs Amer. Math. Soc. vol. 136, No. 651 (1998), 91-118.
42. Counting Hopf Galois structures on non-abelian Galois field extensions (with S. Carnahan), J. Algebra 218 (1999), 81-92.
43. Cyclic Hopf orders defined by isogenies of formal groups (with R. Underwood), American J. Math. 125 (2003), 1295-1334.
44. Duals of formal group Hopf orders (with R. Underwood), Illinois J. Math. 48 (2004), 923-940.
45. Duality for Hopf orders (with R. Underwood), Trans. Amer. Math. Soc. 358 (2006), 1117-1163
46. On Hopf Galois structures and complete groups, New York J. Math. 9 (2003), 99-115.
47. Elementary abelian Hopf Galois structures and polynomial formal groups, J. Algebra 283 (2005), 292-316.
48. Dual Hopf orders in group rings of elementary abelian p-groups (with H. H. Smith III), J. Algebra 294 (2005), 489-518
49. Mathematical reasoning and fast food, NYS Math. Teacher's Journal 55 (2005), 51-54.
50. Some Hopf Galois structures arising from elementary abelian p-groups, Proc. Amer. Math. Soc. 135 (2007), 3453-3460.
51. Cayley's Theorem and Hopf Galois structures arising from semidirect products of cyclic groups (with J. Corradino), J. Algebra 308 (2007), 236-251.
52. Hopf Galois structures on Kummer extensions of prime power degree, New York J. Math. 17 (2011), 51-74.
53. Abelian Hopf Galois structures on Galois field extensions of prime power order (with S. C. Featherstonhaugh and A. Caranti), Trans. Amer. Math. Soc. 364 (2012), 3675-3684.
54. Fixed-point free endomorphisms and Hopf Galois structures, Proc. Amer. Math. Soc. (to appear)
55. Fixed-point free endomorphisms of groups related to finite fields, Finite Fields and their Applications 18 (2012), 661-673.
56. On Hopf Galois structures on Galois extensions of fields (with T. Kohl), preprint, (1/12)
57. Fixed point free pairs of homomorphisms and nonabelian Hopf Galois structures (with N. Byott), New York J. Math. 18 (2012), 707-731.

Other publications

• Helderberg Escarpment Planning Guide, a project of the Helderberg Escarpment Planning Committee (coed. with Daniel A. Driscoll), Albany County Land Conservancy, 2002. Available at www.mohawkhudson.org/pubs.htm .
• "McKownville, News and Comment", a sequence of at least 120 columns appearing in the Altamont Enterprise (Altamont, NY) between 1980 and 1986. Scanned copies of the newspapers are obtainable at historicnewspapers.guilpl.org .