First order conditions are given which are necessary for a commutative regular ring to have a prime integrally closed extension. If the ring is countable these conditions are also sufficient. In [8] an example was given of a commutative regular ring with no prime model extension to a commutative integrally closed regular ring. In this paper we give (in §2) first order conditions which are neces...

We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n− 1)-ring (resp., a weakly (n,n− 1)-ring). We also give a new characterization of n-von Neumann regular rings and a characterization of weak n-von Neumann regular rings for (CH)-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-von Neu...

Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...

The research program of Karl Ernst von Baer (1792-1876) intended to enhance the comparative approach of animal classification by demonstrating vertebrate affinities (homology). Baer visualized his ideas on development and evolution with an unpublished figure of a branching tree. To buttress his reflections on how species-specific embryogenesis produces a branching tree, he worked out a cladogra...

This paper is a continuation of our recent joint work with K.H. Leung on the real spectrum of a noncommutative ring 15]. The object of the present paper is to develop a theory of real places and valuations to accompany the theory of orderings developed in 15]. Because of the existence of integral domains which are not embeddable in a skew eld, it is necessary to deal directly with integral doma...

This paper generalizes slightly a result of Kunz [l ] and Nakai [2]. If R>S are commutative rings with identity we introduce a module D*(R/S) defined as the quotient of the module D(R/S) oí S differentials of A by the submodule consisting of elements which are mapped to zero by every homomorphism of D(R/S) having values in a finitely generated A module. The characteristic exponent of a field is...

‎For the subclasses $mathcal{M}_1$ and $mathcal{M}_2$ of‎ ‎monomorphisms in a concrete category $mathcal{C}$‎, ‎if $mathcal‎{M}_2subseteq mathcal{M}_1$‎, ‎then $mathcal{M}_1$-injectivity‎ ‎implies $mathcal{M}_2$-injectivity‎. ‎The Baer type criterion is about‎ ‎the converse of this fact‎. ‎In this paper‎, ‎we apply injectivity to the classes of $C$-dense‎, ‎$C$-closed‎ ‎monomorphisms‎. ‎The con...

BACKGROUND Transient evoked otoacoustic emissions (TEOAE) are widely used for human neonatal deafness screening, but have not been reported for clinical use in dogs. HYPOTHESIS/OBJECTIVES To investigate the feasibility of TEOAE testing in conscious puppies and the ability of TEOAE testing to correctly identify deaf and hearing ears, as defined by brainstem auditory evoked response (BAER). A...

Introduction. The concept of a local ring was introduced by Krull [7](1), who defined such a ring as a commutative ring 9î in which every ideal has a finite basis and in which the set m of all non-units is an ideal, necessarily maximal. He proved that the intersection of all the powers of m is the zero ideal. If the powers of m are introduced as a system of neighborhoods of zero, then 3Î thus b...