Publications
- The Krull Intersection Theorem II, D.D. Anderson, J.
Matijevic, and W. Nichols, Pacific J. Math. 66(1976), 15-22.
An investigation of the intersection of the powers of an ideal
in a commutative ring.
- Bialgebras of type one, Warren D. Nichols, Comm. Algebra
6(15) (1978), 1521-1552.
A step towards the classification of finite dimensional Hopf
algebras, with the construction of some new ones.
- Quotients of Hopf Algebras, Warren D. Nichols, Comm.
Algebra 6(1978), 1789-1800.
A quotient of a Hopf algebra is, in many situations, a Hopf
algebra itself.
- Pointed irreducible bialgebras, Warren D. Nichols, J.
Algebra 57(1979), 64--76.
Certain bialgebras are characterized as universal objects, and
their structures are determined.
- Left Hopf algebras, James A. Green, Warren D. Nichols, and
Earl J. Taft, J. Algebra 65(1980), 399--411.
A left Hopf algebra is, in many situations, a Hopf algebra itself.
- Differential formal groups of J.F. Ritt, W. Nichols and B.
Weisfeiler, Amer. J. Math. 104(1982), 943-1003.
Hopf-theoretic methods are applied in the classification of
certain Lie algebras.
- Hopf algebras and combinatorics, Warren Nichols and Moss
Sweedler, Contemp. Math. 6, Amer. Math. Soc., 1982, 49-84.
Applications of Hopf methods and results to combinatorics.
- The left antipodes of a left Hopf algebra, Warren D. Nichols
and Earl J. Taft, Contemp. Math., 13, Amer. Math. Soc., 1982, 363-368.
A left Hopf algebra may have no left antipode which is a
bialgebra antimorphism.
- Seminormality in power series rings, J.W. Brewer and Warren
D. Nichols, J. Algebra 82(1983), 282-284.
If R is a seminormal domain, then so is R[[X]].
- The Kostant structure theorems for K/k-Hopf algebras,
Warren D. Nichols, J. Algebra 97(1985), 313-328.
The structure of certain algebras resembling Hopf algebras is
determined.
- Ideals containing monics, Budh Nashier and Warren Nichols,
Proc. Amer. Math. Soc. 99(1987), 634-636.
A new monic lifting theorem is used to give an elementary proof
of Horrocks' Theorem.
- Generators of ideals containing monics, Robert Gilmer,
Budh Nashier, and Warren Nichols, Arch. Math. (Basel) 49(1987),407-413.
A study, with applications, of a situation in which ideals
containing monics are in fact principal.
- Eine rekursive universelle Funktion fuer die primitve
rekursiven Funktionen, Hilbert Levitz and Warren Nichols, Z. Math. Logik
Grundlag. Math. 33(1987), 527-535.
A simple construction of a recursive function which is a
universal function for the primitive recursive functions.
- Patching modules over commutative squares, Budh Nashier
and Warren Nichols, J. Algebra 113(1988), 294-317.
A systematic study of an important technique for constructing
modules.
- On extending endomorphisms to automorphisms, Hilbert Levitz
and Warren Nichols, Internat. J. Math. Math. Sci. 11(1988),231-238.
When monic endomorphisms are extended to automorphisms, a
surprisingly large number of properties are preserved.
- A natural variant of Ackermann's function, Hilbert Levitz
and Warren Nichols, Z. Math. Logik Grundlag. Math. 34(1988), 399-401.
A variant of Ackermann's function which extends to the ordinals
still majorizes the primitive recursive functions.
- Finite dimensional Hopf algebras are free over grouplike
subalgebras, Warren D. Nichols and M. Bettina Zoeller, J. Pure Appl.
Algebra 56(1) (1989), 51-57.
An important structural result for finite dimensional Hopf
algebras.
- The prime spectra of subalgebras of affine algebras and
their localizations, Robert Gilmer, Budh Nashier, and Warren Nichols, J.
Pure Appl. Algebra 57 (1989), 47-65.
The spectra in question share the properties of the spectra of
affine algebras on a Zariski open set, but not globally.
- On the heights of prime ideals under integral extensions,
Robert Gilmer, Budh Nashier, and Warren Nichols, Arch. Math. (Basel)
52(1989), 47-52.
An investigation of the effect of weakening the hypotheses of
the "Going Down" Theorem.
- A Hopf algebra freeness theorem, Warren D. Nichols and M.
Bettina Zoeller, Amer. J. Math. 111(1989), 381-385.
A finite dimensional Hopf algebra is free as a module over each
of its Hopf subalgebras.
- Freeness of infinite dimensional Hopf algebras over
grouplike subalgebras, Warren D. Nichols and M. Bettina Zoeller, Comm.
Algebra 17(2) (1989), 413-424.
If the group is finite solvable, then the Hopf algebra yields a
faithful representation, but as a module it may not be free.
- A duality theorem for Hopf module algebras, Chen Cao-yu and
Warren D. Nichols, Comm. Algebra, Comm. Algebra 18(10) (1990), 3209-3221.
A generalization of a structure theorem of Blattner and Montgomery.
- The structure of the dual Lie coalgebra of the Witt
algebra, Warren D. Nichols, J. Pure Appl. Algebra 68 (1990), 359-364.
When the characteristic of the field is not 2, the dual of the
Witt algebra is the space of linearly recursive sequences.
- A note on perfect rings, Budh Nashier and Warren Nichols,
Manuscripta Math. 70 (1991), 307-310.
A proof of a conjecture of Neggers, a counterexample to a
conjecture of Neggers, and a counterexample to a result of Rant.
- A macro program for the primitive recursive functions,
Hilbert Levitz and Warren Nichols, Z. Math. Logik Grundlag. Math. 37
(1991), 121-124.
A quick demonstration that a universal function for the
primitive recursive functions is recursive.
- On Steinitz properties, Budh Nashier and Warren Nichols,
Arch. Math. (Basel) 57 (1991), 247-253.
A study of rings for which a version of the Steinitz replacement
theorem holds.
- Freeness of infinite dimensional Hopf algebras, Warren D.
Nichols and M. Bettina Richmond, Comm. Algebra 20(5) (1992), 1489-1492.
If B is a finite dimensional semisimple Hopf subalgebra of
H, then every infinite dimensional (H,B) - Hopf module is free as a
B-module.
- On Lie and associative duals, Warren D. Nichols, J. Pure
Appl. Algebra 87 (1993), 313-320.
An isomorphism between certain duals yields a sought-after
formula for the Lie coproduct of a linearly recursive sequence.
- Cosemisimple Hopf Algebras, Warren D. Nichols, in Advances
in Hopf Algebras, Marcel Dekker (1994), 135-151.
A simplified, self-contained account of some important recent
results.
- The Grothendieck group of a Hopf Algebra, J. Pure Appl.
Algebra 106 (1996), 297-306.
New Hopf algebra techniques yield a proof of a special case of a
Kaplansky conjecture.
- On series of ordinals and combinatorics, J.P. Jones, H.
Levitz, and W.D. Nichols, Math. Logic Quart. 43 (1997), 121-133.
Formulae for finding ordinal sums, with applications to the
evaluation of generalized binomial coefficients.
- The Grothendieck algebra of a Hopf algebra, I, Warren D.
Nichols and M. Bettina Richmond, Comm. Algebra 26(4) (1998), 1081-1095.
The development of representation theory aimed at resolving a conjecture of Kaplansky about cosemisimple Hopf algebras.
- Multiplicative groups of fields, Maria Contessa, Joe L. Mott, and Warren D. Nichols,
in Advances in Commutative Ring Theory, Dekker
Lecture Notes in Pure and Applied Math 205 (1999), 197-216.
Results pertaining to the classical problem of determining which abelian groups can be the multiplicative group of a field.
- Algebraic Myhill-Nerode Theorems, Warren D. Nichols and Robert G. Underwood, Theoret. Comput. Sci. 412 (2011) 448-457.
Versions of the celebrated Myhill-Nerode Theorem, in which certain algebras, coalgebras, and bialgebras (with additional structure) play the role of the finite automata.
- The number of convex sets in a product of totally ordered sets, Brandy Barnette, Warren Nichols and Tom Richmond,
to appear in Rocky Mountain J. Math. 49(1) (2019).
A formula for the number of convex sets in a product of two finite totally ordered sets, and related results.