EUDML

Currently displaying 1 – 11 of 11

Order by Relevance | Title | Year of publication

A structure theory for semialgebraic extensions of division algebras.

Carl Faith — 1962

Journal für die reine und angewandte Mathematik

Polynomial rings over Jacobson-Hilbert rings.

Carl Faith — 1989

Publicacions Matemàtiques

A ring R is (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a ring R is again . In this paper we show this is not the case.

Rings with zero intersection property on annihilators: Zip rings.

Carl Faith — 1989

Publicacions Matemàtiques

Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent: (ZIP 1) If the right anihilator X^⊥ of a subset X of R is zero, then X₁ ^⊥ = 0 for a finite subset X₁ ⊆ X. (ZIP 2) If L is a left ideal and if L^⊥ = 0, then L₁

Addendum to .

Carl Faith — 1992

Publicacions Matemàtiques

We list some typos and minor correction that in no way affect the main results of (Publicacions Matemàtiques 33, 2 (1989), pp. 329-338), e.g., nothing stated in the abstract is affected.

Embedding torsionless modules in projectives.

Carl Faith — 1990

Publicacions Matemàtiques

In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring R is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.

Rings whose modules have maximal submodules.

Carl Faith — 1995

Publicacions Matemàtiques

A ring R is a right max ring if every right module M ≠ 0 has at least one maximal submodule. It suffices to check for maximal submodules of a single module and its submodules in order to test for a max ring; namely, any cogenerating module E of mod-R; also it suffices to check the submodules of the injective hull E(V) of each simple module V (Theorem 1). Another test is transfinite nilpotence of the radical of E in the sense that rad^α E = 0; equivalently,...

Addendum to .

Carl Faith — 1998

Publicacions Matemàtiques

Addendum to the author's article "Rings whose modules have maximal submodules", which appeared in Publicacions Matemàtiques 39, 1 (1995), 201-214.

Self-injective Von Neumann regular subrings and a theorem of Pere Menal.

Carl Faith — 1992

Publicacions Matemàtiques

This paper owes its origins to Pere Menal and his work on Von Neumann Regular (= VNR) rings, especially his work listed in the bibliography on when the tensor product K = A ⊗ B of two algebras over a field k are right self-injective (= SI) or VNR. Pere showed that then A and B both enjoy the same property, SI or VNR, and furthermore that either A and B are algebraic algebras over k (see [M]). This is connected with a lemma in the proof of the , namely a finite ring extension K = k[a, ..., a] is...

New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith — 1996

Publicacions Matemàtiques

A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.