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Remarks on principal ideal ringsSome of the next articles are maybe not open access.
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Mathematics of the USSR-Sbornik, 1973
Every such ring is a direct sum of matrix rings over finite completely primary principal ideal rings. These latter rings are called Galois-Eisenstein-Ore rings or GEO-rings. A number of defining properties for GEO-rings are given, from which it follows that a finite ring with identity in which every two-sided ideal is left principal is a principal ...
A. A. Nečaev
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Every such ring is a direct sum of matrix rings over finite completely primary principal ideal rings. These latter rings are called Galois-Eisenstein-Ore rings or GEO-rings. A number of defining properties for GEO-rings are given, from which it follows that a finite ring with identity in which every two-sided ideal is left principal is a principal ...
A. A. Nečaev
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Lexicodes over finite principal ideal rings
Designs, Codes and Cryptography, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jared Antrobus, Heide Gluesing-Luerssen
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The Factor Ring Structure of Quadratic Principal Ideal Domains
The American mathematical monthly, 2023Previous authors have classified the possible factor rings of the Gaussian integers and the Eisenstein integers. Here, we extend this classification to the ring of integers of any quadratic number field, provided the ring has unique factorization. In the
John Greene, Weizhi Jing
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Subrings of the power series ring over a principal ideal domain
, 2021Let D be a principal ideal domain (PID), I be an ideal of D, and X be an indeterminate over D. Let [D;I][X] be the subring of the power series ring consisting of all power series in such that for all large i.
G. Chang, Phan Thanh Toan
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Approximations of Maximal and Principal Ideal
Social Science Research Network, 2020In this paper, we will be delving deeper into the connection between the rough theory and the ring theory precisely in the principle and maximal ideal.
Faraj. A. Abdunabi
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Canadian Mathematical Bulletin, 1976
This paper determines the structure of finite rings whose two sided ideals are principal as left ideals, and as right ideals. Such rings will be called principal ideal rings. Although finite rings have been studied extensively [1], [5], [12], [14] and the tools necessary for describing finite principal ideal rings have been available for thirty years ...
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This paper determines the structure of finite rings whose two sided ideals are principal as left ideals, and as right ideals. Such rings will be called principal ideal rings. Although finite rings have been studied extensively [1], [5], [12], [14] and the tools necessary for describing finite principal ideal rings have been available for thirty years ...
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QUASI-COMMUTATIVE PRINCIPAL IDEAL RINGS
The Quarterly Journal of Mathematics, 1986An element u in an associative ring R with identity is normalising if \(Ru=uR\). A quasi-commutative principal ideal ring (QCPIR) is a ring in which every two-sided ideal is generated by a normalising element. The author develops a detailed structure theory for QCPIRs, including the following results: any QCPIR is uniquely a finite direct sum of ...
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Modules Over Principal Ideal Rings
2021One result that greatly simplifies undergraduate linear algebra is that vector spaces over a field have a basis. This allows us to perform computations in coordinates, as well as to representat linear maps by matrices. Over a ring which is not a field, there exist modules which are not free, and the classification of modules over general rings is much ...
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Parainjectivity, paraprojectivity and artinian principal ideal rings
Journal of Algebra and Its Applications, 2019In this work, we introduce the concepts of parainjectivity and paraprojectivity. We give some basic properties about them and we obtain some characterizations of artinian principal ideal rings.
Alvarado-García, Alejandro +2 more
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