2000/01 The Andrews-Curtis conjecture, a problem on locally finite groups, some aspects of Grigorchuk groups, and the paper 'Algebraic Geometry over Groups' by G. Baumslag, A. Myasnikov, and V. Remeslennikov which appeared in J. Algebra 219 (1999). 2000/01 The Andrews-Curtis conjecture, a problem on locally finite groups, some aspects of Grigorchuk groups, and the paper 'Algebraic Geometry over Groups' by G. Baumslag, A. Myasnikov, and V. Remeslennikov which appeared in J. Algebra 219 (1999).

Algebraic Geometry over Groups I. Algebraic Sets and Ideal Theory*1 Gilbert Baumslaga, *, Alexei Myasnikovb, and Vladimir Remeslennikovc a City College of New York, New York, New York, 10031 b City College of New York, New York, New York, 10031 c Omsk University, Omsk, Russia Received 8 January 1999. Available online 10 April 2002. Abstract The object of this paper, which is the first in a series of three, is to lay the foundations of the theory of ideals and algebraic sets over groups. References AL. L. Auslander, On a problem of Philip Hall. Ann. of Math. (2) 86 (1967), pp. 112–116. MathSciNet BH. H. Bass, Groups acting on non-archimedian trees. Arboreal Group Theory (1991), pp. 69–130. BB. B. Baumslag, Residually free groups. Proc. London Math. Soc. 17 (1967), pp. 402–418. MathSciNet BG. G. Baumslag, On generalized free products. Math. Z. 7 (1962), pp. 423–438. MathSciNet BMR1. G. Baumslag, A. Myasnikov and V. 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