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Generalized Baer $ \ast $-Rings
Siberian Mathematical Journal, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M Ahmadi, A Moussavi
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Rings which are Baer or quasi-Baer modulo a radical
Communications in Algebra, 2021Baer and quasi-Baer rings are important classes of algebraic objects, and their properties have roots in analysis.
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Journal of Algebra and Its Applications, 2018
We say a ring [Formula: see text] is [Formula: see text]-Baer if the right annihilator of every projection invariant left ideal of [Formula: see text] is generated by an idempotent element of [Formula: see text]. In this paper, we study connections between the [Formula: see text]-Baer condition and related conditions such as the Baer, quasi-Baer and ...
Kara, YELİZ +2 more
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We say a ring [Formula: see text] is [Formula: see text]-Baer if the right annihilator of every projection invariant left ideal of [Formula: see text] is generated by an idempotent element of [Formula: see text]. In this paper, we study connections between the [Formula: see text]-Baer condition and related conditions such as the Baer, quasi-Baer and ...
Kara, YELİZ +2 more
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Baer duality for commutative rings
Forum Mathematicum, 2002Let \(R\) and \(T\) be rings, and let \(_RU_T\) be a bimodule faithful on both sides. The triple \((R,{_RU_T},T)\) is a Baer duality if \({\mathcal L}({_RR})\) and \({\mathcal L}(U_T)\), as well as \({\mathcal L}({_RU})\) and \({\mathcal L}(T_T)\), are respectively anti-isomorphic, where \({\mathcal L}(X)\) denotes the submodule lattice of a module \(X\
ÁNH P. N., HERBERA D., MENINI, Claudia
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Baer and Quasi-Baer Differential Polynomial Rings
Communications in Algebra, 2008A ring R with a derivation δ is called δ-quasi Baer (resp. quasi-Baer), if the right annihilator of every δ-ideal (resp. ideal) of R is generated by an idempotent, as a right ideal. We show the left-right symmetry of δ-(quasi) Baer condition and prove that a ring R is δ-quasi Baer if and only if R[x;δ] is quasi Baer if and only if R[x;δ] is -quasi Baer
A. R. Nasr-Isfahani, A. Moussavi
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Mathematica Slovaca, 2015
Abstract Let α denote an infinite cardinal or ∞ which is used to signify no cardinal constraint. This work introduces the concept of an αcc-Baer ring and demonstrates that a commutative semiprime ring A with identity is αcc-Baer if and only if Spec(A) is αcc-disconnected. Moreover, we prove that for each commutative semprime ring A with
Carrera, Ricardo Enrique +3 more
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Abstract Let α denote an infinite cardinal or ∞ which is used to signify no cardinal constraint. This work introduces the concept of an αcc-Baer ring and demonstrates that a commutative semiprime ring A with identity is αcc-Baer if and only if Spec(A) is αcc-disconnected. Moreover, we prove that for each commutative semprime ring A with
Carrera, Ricardo Enrique +3 more
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BAER ENDOMORPHISM RINGS AND ENVELOPES
Journal of Algebra and Its Applications, 2010R is called a Baer ring if the left annihilator of every nonempty subset of R is a direct summand of RR. R is said to be a left AFG ring in case the left annihilator of every nonempty subset of R is a finitely generated left ideal. In this paper, we study Baer rings and AFG rings of endomorphisms of modules in terms of envelopes.
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Communications in Algebra, 1997
In this paper we give counterexamples to the following questions: (1) Are commutative reduced rings Baer?, (2) Are commutative von Neumann regular rings Baer?, (3) Are reduced rings with center Baer also Baer?, and (4) Are prime Pi-rings Baer? Moreover we consider some conditions under which the answers of them are affirmative.
Yang Lee, Nam Kyun Kim, Chan Yong Hong
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In this paper we give counterexamples to the following questions: (1) Are commutative reduced rings Baer?, (2) Are commutative von Neumann regular rings Baer?, (3) Are reduced rings with center Baer also Baer?, and (4) Are prime Pi-rings Baer? Moreover we consider some conditions under which the answers of them are affirmative.
Yang Lee, Nam Kyun Kim, Chan Yong Hong
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