Besides giving an introduction to Commutative Algebra-the theory of c-mutative rings-this
book is devoted to the study of projective modules and the minimal number of generators of …

In these notes on" Projective Modules and Complete Intersections" an account on the recent
developments in research on this subject is presented. The author's preference for the …

Let A be a smooth affine domain of dimension n over a field k and I be a prime ideal of A [T]
of height r such that A [T]/I is smooth and 2r≥ n+ 3. Let f1 (T),···, fr (T)∈ I such that I=(f1 (T) …

Let A be a smooth affine domain of dimension d over an infinite perfect field k and let n be an
integer such that 2n⩾ d+ 3. Let I⊂ A [T] be an ideal of height n. Assume that I=(f1 …

In the first section we develop a method useful for proving the existence of unimodular
elements, and in the second section we study the action of an elementary group on the …

Let $ R $ be a commutative ring, ${\mathbf {v}}(X) $ a unimodular $ n $-vector $(n\geqslant
3) $ over $ R [X] $. Suppose the leading coefficients in ${\mathbf {v}}(X) $ form a unimodular …

THE UNIVERSITY OF CHICAGO Date kUCrUST^ 9^ RATk _______________ g-^^ APR-^ L
1461 Author Birth Date NOkJ VANISHING-SEcTToMS OF ALtrESRAK Vt-dO «Title of …

Let R be a commutative noetherian ring of dimension d and M be a commutative,
cancellative, torsion-free monoid of rank r. Then Sd im (R [M])≤ max {1, dim (R [M])− 1} …

In [13, Section 5], Murthy defined the “Segre class” of a finitely generated module M over a
smooth affine domain A over an algebraically closed field k. The Segre class of M, denoted …

A Survey of Problems and Results on the Number of Defining Equations §o. Introduction.
How many equations are necessary to defi Page 1 A Survey of Problems and Results on …