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(i) ÌÏÍÏÂÒÀ×ÉÄÁÉ
1. Serre’s generalized problem for affine rings. Generated by monomials. (Russian) Tbilisi University Press, Tbilisi, 1982.
(ii) ÓÀÌÄÝÍÉÄÒÏ ÓÔÀÔÉÄÁÉ
Subrings of the ring of polynomials generated by monomials. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 104 (1981), No. 3, 545-547.
Generalized Serre problem for affine rings generated by monomials. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 106 (1982), No. 1, 29-32.
Projective modules over seminormal rings generated by monomials. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 114 (1984), No. 3, 473-475.
Triviality of the groups SK_{0} and Pic for algebras generated by monomials, and Hermitian seminormal rings. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 117 (1985), No. 1, 29-32.
Projective modules over affine rings, generated by monomials. (Russian) Tbilisi University Press, Tbilisi, 1985, 24-43.
On the division class groups of divisible monoids. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 122 (1986), No. 2, 241-244.
On polynomial functions and polynomial algebras. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 125 (1986), 25-27.
Anderson’s conjecture and projective modules over monoid algebras. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 125 (1986), 289-291.
On the K-theory of complete projective algebras. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 128 (1987), No. 1, 17-20.
The Anderson conjecture and a maximal class of monoids over which projective modules are free. (Russian) Mat. Sb. (N.S.) 135(177) (1988), No. 2, 169-185, English transl.: Math. USSR-Sb. 63 (1989), No. 1, 165-180.
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Classical algebraic K-theory of monoid algebras. K-theory and homological algebra (Tbilisi, 1987-88), 36-94, Lecture Notes in Math., 1437, Springer, Berlin, 1990.
The elementary action on unimodular rows over a monoid ring. J. Algebra 148 (1992), No. 1, 135-161.
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Geometric and algebraic representations of commutative cancellative monoids. Proc. A. Razmadze Math. Inst. 113 (1995), 31-81.
Nontriviality of SK_{1}(R[M]). J. Pure Appl. Algebra 104 (1995), 169-190.
The isomorphism problem for monoid rings of rank 2 monoids. J. Pure Appl. Algebra 105 (1995), 17-51.
Combinatorial invariance of Stanley-Reisner rings (with W. Bruns). Georgian Math. J. 3 (1996), 315-318.
Normal polytopes, triangulations, and Koszul algebras (with W. Bruns and and N. V. Trung). J. Reine Angew. Math. 485 (1997), 123-160.
The isomorphism problem for commutative monoid rings. J. Pure Appl. Algebra 129 (1998), No. 1, 35-65.
Examples of infinitely generated Koszul algebras (with W. Bruns). Math. Nachr. 195 (1998), 47-59.
Toric degenerations and vector bundles. Proc. Amer. Math. Soc. 127 (1999), 3493-3494.
K-theory of affine toric varieties. Homology Homotopy Appl. 1 (1999), 135-145.
A regularity criterion for semigroup rings (with W. Bruns). Georgian Math. J. 6 (1999), No. 3, 259-262.
Rectangular simplicial semigroups (with W. Bruns). Commutative algebra, algebraic geometry, and computational methods (Hanoi, 1996), 201-213, Springer, Singapore, 1999.
Polytopal linear groups (with W. Bruns). J. Algebra 218 (1999), No. 2, 715-737.
Normality and covering properties for affine semigroups (with W. Bruns). J. Reine Angew. Math. 510 (1999), 161-178.
A Counterexample to an integral analogue of Carathéodory theorem (with W. Bruns, M. Henk, A. Martin, and R. Weismantel). J. Reine Angew. Math. 510 (1999), 179-185.
Regular analytic transformations of R^{2}. Ann. Polon. Math. 75 (2000), 99-109.
Subintegral extensions and unimodular rows. Geometric and combinatorial aspects of commutative algebra (Messina, 1999), 221-225, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York, 2001.
Polytopal linear retractions (with W. Bruns). Trans. Amer. Math. Soc. 354 (2002), 179-203.
Polyhedral algebras, arrangements of toric varieties, and their groups (with W. Bruns). Computational commutative algebra and combinatorics (Osaka, 1999), 1-51, Adv. Stud. Pure Math., 33, Math. Soc. Japan, Tokyo, 2002.
Semigroup rings and discrete geometry (with W. Bruns). Sémin. Congr. 6 (2002), 43-127.
Polytopal linear algebra (with W. Bruns). Beiträge Algebra Geom. 43 (2002), No. 2, 479-500.
Unimodular covers of multiples of polytopes (with W. Bruns). Doc. Math. 7 (2002), 463-480.
Polyhedral K_{2 }(with W. Bruns). Manuscripta Math. 109 (2002), No. 3, 367-404.
Problems and algorithms for affine semigroups (with W. Bruns and N. V. Trung). Semigroup Forum 64 (2002), 180-212.
Divisorial linear algebra of normal semigroup rings (with W. Bruns). Algebr. Represent. Theory 6 (2003), 139-168.
Higher polyhedral K-groups (with W. Bruns). J. Pure Appl. Algebra (to appear).
Higher K-theory of toric varieties. K-Theory (to appear).
Toric varieties with huge Grothendieck group. Adv. Math. (to appear).
The nilpotence conjecture in K-theory of toric varieties (submitted).
Smooth toric varieties and quadratic embeddings (with S. Hosten). (in preparation).
Abelization of the automorhpism groups of formal power series rings (with Z. Mushkudiani). (in preparation).
Polytopes, Rings, and K-Theory (with W. Bruns). (book in preparation).
K-Theory of Toric Varieties. (book in preparation).