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.