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The Structure of Local Rings with Singleton Basis and Their Enumeration

Mathematics, 2022
A local ring is an associative ring with unique maximal ideal. We associate with each Artinian local ring with singleton basis four invariants (positive integers) p,n,s,t.
Yousef Alkhamees, Sami Alabiad
doaj   +3 more sources

On Local Rings [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2014
A ring R is called local ring if it has exactly one maximal ideal. In this paper, we introduce some characterization and basic properties of this ring. Also, we studied the relation between local rings and Von Neumann regular rings and strongly regular ...
Zubayda Ibraheem, Anees Fthee
doaj   +2 more sources

On Linear Codes over Finite Singleton Local Rings

Mathematics
The study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings.
Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori   +2 more
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Full Classification of Finite Singleton Local Rings

Axioms
The main objective of this article is to classify all finite singleton local rings, which are associative rings characterized by a unique maximal ideal and a distinguished basis consisting of a single element.
Sami Alabiad, Yousef Alkhamees
doaj   +3 more sources

Frobenius Local Rings of Length 5 and Index of Nilpotency 3

Mathematics
This paper investigates finite local non-chain rings associated by the well-known invariants p,n,m,l, and k, where p is a prime number. In particular, we provide a comprehensive characterization of Frobenius local rings of length l=5 and index of ...
Sami Alabiad, Alhanouf Ali Alhomaidhi
doaj   +3 more sources

Finite Local Rings of Length 4

Axioms
This paper presents a comprehensive characterization of finite local rings of length 4 and with residue field Fpm, where p is a prime number. Such rings have an order of p4m elements.
Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori   +2 more
doaj   +3 more sources

['حول الحلقات المحلیة', 'On Local Rings'] [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2014
Zubayda M. Ibraheem, Anees A. Fthee
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Locally Compact Rings [PDF]

Proceedings of the National Academy of Sciences, 1935
As a generalization of theorems of L. Pontryagin, E. R. van Kampen and D. van Dantzig, the authors prove the following theorems: Theorem I: A locally compact and separable (not necessarily associative or commutative) field \(F\) is either a hypercomplex system over the real field or is totally disconnected. Theorem III: A locally compact, separable and
Jacobson, Nathan, Taussky, O.
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Rings of Fractions and Localization [PDF]

Formalized Mathematics, 2020
Summary This article formalized rings of fractions in the Mizar system [3], [4]. A construction of the ring of fractions from an integral domain, namely a quotient field was formalized in [7]. This article generalizes a construction of fractions to a ring which is commutative and has zero divisor
openaire   +3 more sources

Some results on PIT and GPIT theorems [PDF]

Journal of Hyperstructures, 2016
In this paper we generalize the P IT and the GP IT that can be used to study the heights of prime ideals in a general commutative Noetherian ring R and the dimension theory of such a ring and we use these generalizations to prove some useful results.
M. Ebrahimpour
doaj   +1 more source