Results 11 to 20 of about 326,550 (311)

On the structure of principal ideal rings [PDF]

Pacific Journal of Mathematics, 1968
Thomas W. Hungerford
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The Structure of Finite Local Principal Ideal Rings [PDF]

Communications in Algebra, 2012
A ring $R$ is called a PIR, if each ideal of $R$ is a principal ideal. An local ring $(R,\mf{m)}$ is a artinian PIR if and only if its maximal ideal $\mf{m}$ is principal and has finite nilpotency index. In this paper, we determine the structure of a finite local PIR.
Tongsuo Wu, Houyi Yu, Dancheng Lu
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Semigroup Algebras That Are Principal Ideal Rings

Journal of Algebra, 1996
AbstractIt is shown that a semigroup algebraK[S] which is a principal left ideal ring is a finitely generated PI-algebra of Gelfand–Kirillov dimension at most 1. A complete description of principal (left and right) ideal ringsK[S], and of the underlying semigroupsS, is obtained.
Eric Jespers, Jan Okniński
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Finite Principal Ideal Rings [PDF]

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 ...
James L. Fisher
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Matrices with elements in a principal ideal ring [PDF]

Bulletin of the American Mathematical Society, 1933
C. C. MacDuffee
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Finite local principal ideal rings

, 2023
Every finite local principal ideal ring is the homomorphic image of a discrete valuation ring of a number field, and is determined by five invariants. We present an action of a group, non-commutative in general, on the set of Eisenstein polynomials, of degree matching the ramification index of the ring, over the coefficient ring.
Matthé van der Lee
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Characterization of irreducible polynomials over a special principal ideal ring [PDF]

Mathematica Bohemica, 2023
A commutative ring $R$ with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length $e$ is the index of nilpotency of its maximal ideal. In this paper, we show
Brahim Boudine
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Rings with minimum condition on principal ideals [PDF]

Archiv der Mathematik, 1959
Carl Faith
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PILP-rings and fuzzy ideals [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2009
In this paper, we study rings whose principal right ideals are left pure. Also we shall introduce the concept of a fuzzy bi-ideal in a ring, and give some properties of such fuzzy ideals. We also give a characterization of whose principal right ideal are
Raida Mahmood
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About weak $\pi$-rings

Boletim da Sociedade Paranaense de Matemática, 2022
As in \cite{J}, a ring is called a weak $\pi$-ring if every regular principal ideal is a finite product of prime ideals. In this paper, we establish some characterizations for weak $\pi$-rings. Also, we translate the properties weak $\pi$-ring and $(*)$-
Najib Mahdou, Sanae Moussaoui
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