- 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
- 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
- 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
- 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
- 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
- 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)
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
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
- 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
- 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
- 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
- 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.