### 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, Third Edition, 2009.
- 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.
- Cryptology and Error Correction, An Algebraic Introduction, xv + 433 pages, under review
(August, 2017)

#### Professional Publications

On automorphisms of separable algebras (with F. R. DeMeyer), Pacific J. Math. 23 (1967), 25-34.
A note on the fixed ring of a Galois extension, Osaka J. Math 4 (1967), 173-175.
On projective modules and automorphisms of central separable algebras, Canadian J. Math. 21 (1969), 44-53.
The exact sequence of low degree and normal algebras, Bull. Amer. Math. Soc. 76 (1970), 1121-1124.
Abelian Galois extensions of rings containing roots of unity, Illinois J. Math. 15 (1971), 273-280.
On covering spaces and Galois extensions, Pacific J. Math. 37 (1971), 29-33.
On normal Azumaya algebras and the Teichmuller cocycle map, J. Algebra 23 (1972), 1-17.
The Brauer group of graded Azumaya algebras (with G. Garfinkel and M. Orzech), Trans. Amer. Math. Soc. 175 (1973),
299-326.
Mayer-Vietoris sequences and Brauer groups of non-normal domains, Trans. Amer. Math. Soc. 196 (1974), 51-67.
Brauer groups of affine rings, in Ring Theory, Proceedings of the Oklahoma Conference, Marcel Dekker, 1974, 83-93.
The Picard invariant of principal homogeneous spaces (with A. Magid), J. Pure Appl. Algebra 4 (1974), 273-286.
The Brauer group of graded Azumaya algebras II: graded Galois extensions, Trans. Amer. Math. Soc. 204 (1975), 137-
160.
On the Brauer group and factoriality of normal domains (with G. Garfinkel and M. Orzech), J. Pure Appl. Algebra 6
(1975), 111-123.
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.
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.
On Brauer groups of some normal local rings, Brauer Groups, Evanston, 1975, Springer Lecture Notes in Math. 549
(1976), 1-15.
The group of unramified Kummer extensions of prime degree, Proc. London Math. Soc. 35 (1977), 407-422.
Linearizing of n-ic forms and generalized Clifford algebras, Linear and Multilinear Algebra 5 (1978), 267-278.
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.
Stickelberger relations and tame extensions of prime degree, Illinois J. Math 25 (1981), 258-266.
On modular group rings, normal bases and fixed points (with M. Orzech), American Mathematical Monthly 88 (1981),
142-145.
A Stickelberger condition on cyclic Galois extensions, Canadian J. Math. 34 (1982), 686-690.
Tame Kummer extensions and Stickelberger conditions, Illinois J. Math. 28 (1984), 547-554.
Cyclic Stickelberger cohomology and descent of Kummer extensions, Proc. Amer. Math. Soc. 90 (1984), 505-510.
Tameness and local normal bases for objects of finite Hopf algebras (with S. Hurley), Trans. Amer. Math. Soc. 298
(1986), 763-778.
Products of Galois objects and the Picard invariant map, Math J. Okayama Univ.28 (1986) 29-36. .
Representing classes in the Brauer group of quadratic number rings as smash products, Pacific J. Math. 129 (1987),
243-255.
Taming wild extensions with Hopf algebras, Trans. Amer. Math. Soc. 304 (1987), 111-140.
Non-isomorphic equivalent Azumaya algebras, Canadian Math. Bull. 30 (1987), 340-343.
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.
On the Hopf Galois theory for separable field extensions, Comm. Algebra 17 (1989), 809-825.
Azumaya algebras which are not smash products, Rocky Mountain J. Math. 20 (1990), 75-89.
Congruence-torsion subgroups of dimension one formal groups (with Karl Zimmermann), J. Algebra 170 (1994), 929-
955.
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.
Galois extensions over local number rings, in Rings, Extensions and Homology, (A. Magid, ed.), Marcel Dekker, 1994,
41-66.
Hopf Galois structures on degree p^2 extensions of local fields, New York J. Math. 2 (1996), 86-102.
Introduction to polynomial formal groups and Hopf algebras, Memoirs Amer. Math. Soc. vol. 136, No. 651 (1998),
1-10.
Dimension one polynomial formal groups (with D. Moss, J. Sauerberg), Memoirs Amer. Math. Soc. vol. 136, No. 651
(1998), 11-20.
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.
Degree 2 formal groups and Hopf algebras (with J. Sauerberg), Memoirs Amer. Math. Soc. vol. 136, No. 651 (1998),
55-90.
p-elementary group schemes--construction, and Raynaud's theory
(with C. Greither), Memoirs Amer. Math. Soc. vol.
136, No. 651 (1998), 91-118.
Counting Hopf Galois structures on non-abelian Galois field
extensions (with S. Carnahan), J. Algebra 218 (1999),
81-92.
Cyclic Hopf orders defined by isogenies of formal groups (with R.
Underwood), American J. Math. 125 (2003), 1295-1334.
Duals of formal group Hopf orders (with R. Underwood), Illinois
J. Math. 48 (2004), 923-940.
Duality for Hopf orders (with R. Underwood), Trans. Amer. Math.
Soc. 358 (2006), 1117-1163
On Hopf Galois structures and complete groups, New York J. Math. 9
(2003), 99-115.
Elementary abelian Hopf Galois structures and polynomial formal
groups, J. Algebra 283 (2005), 292-316.
Dual Hopf orders in group rings of elementary abelian p-groups (with
H. H. Smith III), J. Algebra 294 (2005), 489-518
Mathematical reasoning and fast food, NYS Math. Teacher's Journal 55
(2005), 51-54.
Some Hopf Galois structures arising from elementary abelian
p-groups, Proc. Amer. Math. Soc. 135 (2007), 3453-3460.
Cayley's Theorem and Hopf Galois structures arising from semidirect
products of cyclic groups (with J. Corradino), J. Algebra 308 (2007),
236-251.
Hopf Galois structures on Kummer extensions of prime power degree, New
York J. Math. 17 (2011), 51-74.
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.
Fixed-point free endomorphisms and Hopf
Galois structures, Proc. Amer. Math. Soc. 141 (2013), 1255-1265.
Fixed-point free endomorphisms of groups related
to finite fields, Finite Fields and their Applications 18 (2012), 661-673.
Fixed point free pairs of homomorphisms and nonabelian Hopf Galois
structures (with N. Byott), New York J. Math. 18 (2012), 707-731.
Scaffolds and generalized Galois module structure (with N. Byott and G. Elder),
arxiv:1308.2088. To appear, Ann. Inst. Fourier, Gtenoble.
On abelian Hopf Galois structures and finite commutative nilpotent rings,
New York J. Math. 21 (2015), 205-230.
Obtaining abelian Hopf Galois structures from finite commutative
nilpotent rings, arxiv: 1604.05269.
On the Galois correspondence for Hopf Galois extensions, arxiv:
1604.06066. New York J. Math. 23 (2017), 1-10.
Bounds on the number of ideals in finite commutative nilpotent F_p-algebras (with C. Greither),
arxiv: 1706.02518.
#### 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 .

Revised 8/17