Recent Preprints

Levels of cancellation for monoids and modules (with P. Ara, P.P. Nielsen, K.C. O'Meara, E. Pardo, and F. Perera) arXiv
Regular ring properties degraded through inverse limits (with P. Ara, K.C. O'Meara, E. Pardo, and F. Perera), J. Algebra 664 (2025) 365-397 arXiv
The separativity problem in terms of varieties and diagonal reduction (with P. Ara, P.P. Nielsen, E. Pardo, and F. Perera), in NonCommutative Rings and their Applications, VIII (A.\ Laghribi and A.\ Leroy, eds.), Contemp. Math. arXiv
Binomial ideals in quantum tori and quantum affine spaces, J. Algebra 657 (2024), 638-674 arXiv
Spectra of quantum algebras, in Recent Advances in Noncommutative Algebra and Geometry (K.A, Brown, T.J. Hodges, M. Vancliff, J.J. Zhang, eds.), Contemp. Math. 801 (2024) 95-109 arXiv
Cluster algebra structures on Poisson nilpotent algebras (with M.T. Yakimov), Memoirs Amer. Math. Soc. No. 1445 (2023), v+100pp. arXiv
Poisson catenarity in Poisson nilpotent algebras (with S. Launois), J. Algebra 611 (2022) 265-284. arXiv
Integral quantum cluster structures (with M.T. Yakimov), Duke Math. J. 170 (2021) 1137-1200. arXiv
Catenarity in quantum nilpotent algebras (with S. Launois), Proc. Amer. Math. Soc. Ser. B 7 (2020) 202-214. arXiv
The Berenstein-Zelevinsky quantum cluster algebra conjecture (with M.T. Yakimov), J. European Math. Soc. 22 (2020) 2453-2509. arXiv
Tauvel's height formula for quantum nilpotent algebras (with T.H. Lenagan and S. Launois), Communic. in Algebra 47 (2019) 4194-4209. arXiv
Closures in varieties of representations and irreducible components (with B. Huisgen-Zimmermann), Algebra and Number Theory 12 (2018) 379-410. arXiv
Understanding finite dimensional representations generically (with B. Huisgen-Zimmermann), in Geometric and Topological Aspects of the Representation Theory of Finite Groups (J.F. Carlson, S. Iyengar, J. Pevtsova, Eds.), Springer Proc. Math. Stat. 242, Springer (2018) Cham, pp. 131-179. arXiv
Twist invariants of graded algebras (with M.T. Yakimov), Contemp. Math. 715 (2018) 141-170. arXiv
Non-affine Hopf algebra domains of Gelfand-Kirillov dimension two (with J.J. Zhang), Glasgow Math. J. 59 (2017) 563-593. arXiv
The realization problem for some wild monoids and the Atiyah problem (with P. Ara), Trans. Amer. Math. Soc. 369 (2017) 5665-5710. arXiv
Quantum cluster algebra structures on quantum nilpotent algebras (with M.T. Yakimov), Memoirs Amer. Math. Soc. No. 1169 (2017) v+119 pp. arXiv
From quantum Ore extensions to quantum tori via noncommutative UFDs (with M.T. Yakimov), Advances in Math. 300 (2016) 672-716. arXiv
Tame and wild refinement monoids (with P. Ara), Semigroup Forum 91 (2015) 1-27. arXiv
The isomorphism problem for multiparameter quantized Weyl algebras (with J.T. Hartwig), Sao Paolo J. Math. Sci. 9 (2015) 53-61 arXiv
Unipotent and Nakayama automorphisms of quantum nilpotent algebras (with M.T. Yakimov), in Commutative Algebra and Noncommutative Algebraic Geometry (II) (D. Eisenbud, et al., eds.), MSRI Publ. 68, Cambridge (2015) Cambridge Univ. Press, pp. 181-212. arXiv
Zariski topologies on stratified spectra of quantum algebras (with K.A. Brown), in Commutative Algebra and Noncommutative Algebraic Geometry (II) (D. Eisenbud, et al., eds.), MSRI Publ. 68, Cambridge (2015) Cambridge Univ. Press, pp. 63-91. arXiv
Quantum cluster algebras and quantum nilpotent algebras (with M.T. Yakimov), Proc. Nat. Acad. Sci. USA 111 (2014) 9696-9703. arXiv
Noetherian Hopf algebras, Glasgow Math. J. 55A (2013) 75-87. arXiv
LU decomposition of totally nonnegative matrices (with T.H. Lenagan), Linear Alg. Applic. 436 (2012) 2554-2566. arXiv
Irreducible components of module varieties: projective equations and rationality (with B. Huisgen-Zimmermann), Contemp. Math. 562 (2012) 141-167. arXiv
Primitive ideals in quantum SL₃ and GL₃ (with T.H. Lenagan), Contemp. Math. 562 (2012) 115-140. pdf or arXiv
Leavitt path algebras of separated graphs (with P. Ara), J. reine angew. Math. 669 (2012) 165-224. arXiv
C*-algebras of separated graphs (with P. Ara), J. Func. Anal. 261 (2011) 2540-2568. arXiv
Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves (with S. Launois and T.H. Lenagan), Math. Zeitschrift 269 (2011) 29-45. arXiv
Totally nonnegative cells and matrix Poisson varieties (with S. Launois and T.H. Lenagan), Advances in Math. 226 (2011) 779-826. arXiv
The Dixmier-Moeglin equivalence and a Gel'fand-Kirillov problem for Poisson polynomial algebras (with S. Launois), Bull. Soc. Math. France 139 (2011) 1-39. pdf or arXiv
Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two (with J.J. Zhang), J. Algebra 324 (2010) 3131-3168. arXiv
Non-simple purely infinite rings (with G. Aranda Pino, F. Perera, and M. Siles Molina), Amer. J. Math. 132 (2010) 563-610. arXiv
Semiclassical limits of quantized coordinate rings, in Advances in Ring Theory (D.V. Huynh and S. Lopez-Permouth, Eds.), Basel (2010) Birkhäuser, pp. 165-204. arXiv
Semiclassical limits of quantum affine spaces (with E.S. Letzter), Proc. Edinburgh Math. Soc. 52 (2009) 387-407. pdf or arXiv
Leavitt path algebras and direct limits, in Rings, Modules and Representations (N.V. Dung, et al., Eds.), Contemp. Math. 480 (2009) 165-187. pdf or arXiv
Poisson structures on affine spaces and flag varieties. II. (with M. Yakimov), Trans. Amer. Math. Soc. 361 (2009) 5753-5780. pdf or arXiv
Homological properties of quantized coordinate rings of semisimple groups (with J. J. Zhang), Proc. London Math. Soc. (3) 94 (2007) 647-671. pdf or arXiv
A Dixmier-Moeglin equivalence for Poisson algebras with torus actions, in Algebra and Its Applications (D. V. Huynh, S. K. Jain, and S. R. Lopez-Permouth, Eds.), Contemp. Math. 419 (2006) 131-154. pdf or arXiv
The closed-point Zariski topology for irreducible representations (with E. S. Letzter), J. Algebra and Applics. 5 (2006) 1-12. pdf or arXiv
Commutation relations for arbitrary quantum minors, Pacific J. Math. 228 (2006) 63-102. pdf or arXiv
Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space (with K. A. Brown and M. Yakimov), Advances in Math. 206 (2006) 567-629. pdf or arXiv
Semilattices of groups and inductive limits of Cuntz algebras (with E. Pardo and F. Wehrung), J. reine angew. Math. 588 (2005) 1-25. dvi or xxx archive
The complete dimension theory of partially ordered systems with equivalence and orthogonality (with F. Wehrung), Memoirs Amer. Math. Soc. No. 831 (2005) viii+1-117. dvi or ps or xxx archive
Simplicity of noncommutative Dedekind domains (with J.T. Stafford), Proc. Amer. Math. Soc. 133 (2005) 681-686. dvi or ps or xxx archive
Stable rank of corner rings (with P. Ara), Proc. Amer. Math. Soc. 133 (2005) 379-386. dvi or ps or xxx archive
Fractional skew monoid rings (with P. Ara, M.A. Gonzalez-Barroso, and E. Pardo), J. Algebra 278 (2004) 104-126. dvi or ps or xxx archive
Quantized coinvariants at transcendental q (with T.H. Lenagan), in Hopf Algebras in Noncommutative Geometry and Physics (Brussels, 2002) (S. Caenepeel and F. Van Oystaeyen, Eds.), New York (2005) Dekker, pp. 155-165. dvi or ps or xxx archive
Quantized coordinate rings and related noetherian algebras, in Proc. 35th. Symposium on Ring Theory and Representation Theory (Okayama, 2002) (Y. Hirano, Ed.), Okayama (2003) Univ. of Okayama, pp. 19-45. ps or xxx archive
Winding-invariant prime ideals in quantum 3x3 matrices (with T.H. Lenagan), J. Algebra 260 (2003) 657-687. dvi or ps or xxx archive
K₀ of purely infinite simple rings (with P. Ara and E. Pardo), K-Theory 26 (2002) 69-100. dvi or ps or xxx archive
Prime ideals invariant under winding automorphisms in quantum matrices (with T.H. Lenagan), Internat. J. Math. 13 (2002) 497-532. dvi or ps or xxx archive
Quantized primitive ideal spaces as quotients of affine algebraic varieties, in Quantum Groups and Lie Theory (Durham, 1999) (A. Pressley, Ed.), London Math. Soc. Lecture Notes 290, Cambridge (2001) Cambridge Univ. Press, pp. 130-148. dvi or ps or xxx archive
The graded version of Goldie's theorem (with J. T. Stafford), in Algebra and its Applications (Athens, OH 1999) (D.V. Huynh, S.K. Jain, and S.T. Lopez-Permouth, Eds.), Contemp. Math. 259 (2000) 237-240. dvi or ps or xxx archive
Periodic flat modules, and flat modules for finite groups (with D.J. Benson), Pacific J. Math. 196 (2000) 45-67. dvi or ps or PJM archive
K₁ of separative exchange rings and C*-algebras with real rank zero (with P. Ara, K.C. O'Meara, and R. Raphael), Pacific J. Math. 195 (2000) 261-275. dvi or ps or xxx archive or PJM archive
Quantum n-space as a quotient of classical n-space (with E.S. Letzter), Trans. Amer. Math. Soc. 352 (2000) 5855-5876. dvi or ps or xxx archive
The first fundamental theorem of coinvariant theory for the quantum general linear group (with T. H. Lenagan and L. Rigal), Publ. Research Inst. Math. Sci. Kyoto 36 (2000) 269-296. dvi or ps or xxx archive
Quantum determinantal ideals (with T.H. Lenagan), Duke Math. J. 103 (2000) 165-190. dvi or ps
Prime ideals in certain quantum determinantal rings (with T.H. Lenagan), in Interactions between Ring Theory and Representations of Algebras (Murcia, 1998) (F. Van Oystaeyen and M. Saorin, Eds.), New York (2000) Dekker, pp. 239-251. dvi or ps or xxx archive
Prime spectra of quantized coordinate rings, in Interactions between Ring Theory and Representations of Algebras (Murcia, 1998) (F. Van Oystaeyen and M. Saorin, Eds.), New York (2000) Dekker, pp. 205-237. dvi or ps or xxx archive
The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras (with E.S. Letzter), Trans. Amer. Math. Soc. 352 (2000) 1381-1403. dvi or ps
Representations of distributive semilattices in ideal lattices of various algebraic structures (with F. Wehrung) (original title: Representations of distributive semilattices by dimension groups, regular rings, C*-algebras, and complemented modular lattices), Algebra Universalis 45 (2001) 71-102. dvi or ps or xxx archive

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