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Artinian Duo Rings and Self-Duality

Proceedings of the American Mathematical Society, 1989
We show that the endomorphism ring of the minimal cogenerator over an Artinian duo ring is still an Artinian duo ring, and that an Artinian duo ring has self-duality if its Jacobson radical is a direct sum of colocal ideals.
Wei Min Xue
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WHEN CF RINGS ARE ARTINIAN

Journal of Algebra and Its Applications, 2013
Let R be a ring, R is called a right ACS ring if the right annihilator of each element is essential in a direct summand of R. We prove that right CF ring is right artinian under right ACS condition. In particular, FGF conjecture is true under right ACS condition.
Li, Wenxi, Chen, Jianlong
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Artinian Groupoid Rings

Semigroup Forum, 1998
Let \(F\) be a field, let \(G\) be a groupoid and let \(FG\) be a corresponding groupoid algebra. The author proves the following interesting theorems. There exists a groupoid \(H\) containing \(G\) as a subgroupoid and such that \(FH\) has three right ideals only.
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A GENERALIZATION OF SEMISIMPLE ARTINIAN RINGS

Journal of Algebra and Its Applications, 2005
We investigate a ring R with the property that for every right R-module M and every ideal I of R the annihilator of I in M is a direct summand of M, and determine conditions under which such a ring is semisimple Artinian.
Hirano, Yasuyuki, Tsutsui, Hisaya
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Stratiform Simple Artinian Rings

Proceedings of the London Mathematical Society, 1986
Various skew fields arise as the division rings of fractions of certain noetherian rings, such as the Weyl algebras or the group rings of polycyclic-by-finite groups. The purpose of the present paper is to provide some coherent theory for such skew fields. The important new concept that is introduced is that of a stratiform simple artinian ring S. Thus,
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On the cardinality of ideals in artinian rings

Archiv der Mathematik, 1988
Let \(R\) be a right Artinian ring and let \(\alpha\) be an infinite cardinal number. The authors' main result shows that \(R\) contains two uniquely determined (two-sided) ideals \(S(\alpha)\) and \(S^*(\alpha)\) such that: (i) \(S(\alpha)\) is the largest right ideal of \(R\) with cardinality less than \(\alpha\), (ii) \(S^*(\alpha)\) is the smallest
Dinh Van Huynh, Nguyen Viet Dung
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Artinian Semigroup-Graded Rings

Bulletin of the London Mathematical Society, 1995
Let \(S\) be a semigroup with no infinite subgroups and let \(R\) be a right Artinian \(S\)-graded ring. We prove that \(R\) necessarily has finite support.
Clase, M. V., Jespers, E., Kelarev, A. V., Okniński, J.   +3 more
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Further characterizations of Artinian rings

Acta Mathematica Hungarica, 2004
The author proves that the following four conditions on the ring \(R\) with prime radical \(N\) are equivalent. a) \(R\) is right Artinian. b) \(R\) has Krull dimension as right \(R\)-module and there does not exist a finitely generated right \(R\)-module \(M\) with \(\text{ann}(M)\) a prime ideal that is torsion with respect to the set of regular ...
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On Subrings of Simple Artinian Rings

Results in Mathematics, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fuchs, P. R., van Wyk, L.
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Unitaries in Simple Artinian Rings

Canadian Journal of Mathematics, 1979
Let R be a 2-torsion free simple artinian ring with involution*. The element u of R is said to be unitary if u is invertible with inverse u*. In this paper we shall be concerned with the subalgebras W of R over its centre Z such that uWu* ⊆ W, for all unitaries u of R.
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