Showing papers in "Journal of Algebra in 1973"

TL;DR: Forster and Swan as mentioned in this paper used the notion of a basic element (in the terminology of Swan) to extend Bass's theorem to the case of finitely generated modules and showed that any torsion-free module over an integrally closed ring is an extension of a free module.

TL;DR: In this article, a two-sided prime ideal of the right Noetherian ring R is associated with a ring of quotients Rp which reduces to the usual localization of R at P when R is commutative.

TL;DR: In this paper, a constructive proof for finite sets is given which yields some information about R itself, and the relationship between this work and the work of Hochster is also investigated further.

TL;DR: In this article, it was shown that if f 1, f 2, f 3, f 4, f 5, f 6, f 7, f 8, f 9, f 10, f 11, f 12, f 13, f 14, f 15, f 16, f 17, f 18, f 19, f 20, f 21, f 22, f 23, f 24, f 25, f 26, f 27, f 28, f 30, f 31, f 32, f 34, f 35, f 36, f 39, f m

TL;DR: In this paper, the authors considered a simple hereditary noethcrian domain L3 with two generators x, y subject to the relation xy -yx = 1, where xy is the ring of polynomials over Cp in an indeterminate y, and y is a ring of noncommutative polynomorphisms over @[y] in an unknown t with

TL;DR: In this paper, the notion of inner ideal was extended to an arbitrary finite dimensional module M for a finite dimensional Lie algebra with non-degenerate symmetric associative bilinear form.

TL;DR: In this paper, the authors associate with each finite chain ring five invariants (integers) and determine (in certain cases) the number of isomorphism classes of rings with given invariants, yielding immediate corollaries for Pappian Hjelmslev planes which are coordinatized by such rings.

TL;DR: In this article, the authors study the projective ideals which are not contained in any minimal prime ideal-they are finitely generated-and then the rings of finitistic projective dimension one, where such ideals admit the aforementioned primary decomposition.

TL;DR: In this article, the authors define a class of elements of order 3 with the property that any two of them either commute or generate A4, A5 or SL2(3) automorphisms.