THOMAS G. LUCAS

Research Interests: Commutative ring theory. In particular, multiplicative ideal theory and integrality properties in rings with zero divisors.

Selected Publications:

1. "t-Linked Overrings and Prufer v-Multiplication Domains," with D.E. Dobbs, E. Houston and M. Zafrullah, Communications in Algebra, 17 (1989), 2835-2852.

2. "Characterizing when R[X] is Integrally Closed," Proceedings of the American Mathematical Society, 105 (1989), 861-867.

3. "Characterizing when R[X] is Integrally Closed II," Journal of Pure and Applied Algebra, 61 (1989), 49-52.

4. "The Complete Integral Closure of R[X]," Transactions of the American Mathematical Society, 330 (1992), 757-768.

5. "On t-Linked Overrings," with D.E. Dobbs, E. Houston, M. Roitman and M. Zafrullah, Communications in Algebra, 20 (1992), 1462-1488.

6. "The Radical Trace Property and Primary Ideals," Journal of Algebra, 184 (1996), 1093-1112.

7. "The Integral Closure of R(X) and R," Communications in Algebra, 25 (1997), 847-872.

8. "Skolem Properties, Value-Functions, and Divisorial Ideals," with P.-J. Cahen, J.-L. Chabert and E. Houston, Journal of Pure and Applied Algebra, 135 (1999), 207-223.

9. "Trace Properties and Integral Domains," with S.-E. Kabbaj and A. Mimouni, Advances in Commutative Ring Theory, (Fez, Morocco 1997), 421-436, Lecture Notes in Pure and Applied Mathematics, 205, Marcel Dekker, 1999.

10. "When is the Dual of an Ideal a Ring?," with S.-E. Kabbaj, E. Houston and A. Mimouni, Journal of Algebra, 225 (2000), 429-450.