Topic
Ring of integers
About: Ring of integers is a research topic. Over the lifetime, 1856 publications have been published within this topic receiving 15882 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the generalized right finite intersection property (GFP) was studied under a weaker condition on annihilators, and generalized right FIP does not go up to polynomial rings, and the 2-by-2 full matrix ring over a domain has GFP.
Abstract: We continue the study of the right finite intersection property under a weaker condition on annihilators, introducing the concept of generalized right finite intersection property (simply, generalized right FIP). We observe the structure of rings with the generalized right FIP and examine the generalized right FIP for various kinds of basic extensions of rings with the property. We show that the generalized right FIP does not go up to polynomial rings, and that the 2-by-2 full matrix ring over a domain has the generalized right FIP. In the process, we also obtain an equivalent condition for which a nonzero polynomial, over the ring of integers modulo n ≥ 2, is a non-zero-divisor.
3 citations
TL;DR: It turns out that transposition invariant words have a simple interpretation by means of elementary group theory and this leads to investigate some properties of the ring of integers modulo n and primitive roots.
3 citations
TL;DR: In this paper, for a one-dimensional formal group over the ring of integers of a local field in the case of small ramification, the arithmetic of the module of roots of the isogeny is studied, as well as the mathematics of the formal module constructed on the maximal ideal of aLocal field containing all the Roots of the Isogeny.
Abstract: In this paper, for a one-dimensional formal group over the ring of integers of a local field in the case of small ramification we study the arithmetic of the module of roots of the isogeny, as well as the arithmetic of the formal module constructed on the maximal ideal of a local field containing all the roots of the isogeny. Bibliography: 5 titles.
3 citations
01 Feb 1956
TL;DR: In this paper, it was shown that the universal right neoring with an identity which generates its additive loop can be obtained from a free monogenic $3-loop by the above construction and a complete analogue of Theorem 4.1 of [2] is obtained for any one of these subvarieties.
Abstract: Introduction. In a recent paper [2] R. H. Bruck has introduced the concept of right neoring and discussed some properties of these systems. In particular, he has considered analogues of certain properties of the ring of integers. This paper is essentially a commentary on Bruck's paper and we generalize some of his results as follows. The construction of the universal right neoring in [2] is applied to the free monogenic $3-loop in any subvariety $3 of the variety of loops and a complete analogue of Theorem 4.1 of [2] is obtained for any one of these subvarieties. Then, using a result similar to those obtained in [5], it is shown that this construction yields uncountably many right neorings with an identity which generates the additive loop of the right neoring. Conversely, every right neoring with an identity which generates its additive loop can be obtained from a free monogenic $3-loop by the above construction. Each of these right neorings has some properties resembling those of the ring of integers. One possible answer is given to the question raised by Bruck concerning the existence of universal right neorings with free additive loop of arbitrary rank. A brief proof is given, using the results of [4; 5], of the cancellation properties of the monogenic universal right neoring. Finally, we discuss briefly the relationship between right neorings and the logarithmetics of Etherington.
3 citations
TL;DR: In this paper, the ring of integers of the pnth cyclotomic field is defined as a unit of a rational integer modulo and η is a power of p depending on the p-adic L-functions attached to it.
3 citations