Results 141 to 150 of about 306,524 (177)

Parainjectivity, Paraprojectivity and Artinian Principal Ideal Rings

Journal of Algebra and Its Applications, 2019
In 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.
Alejandro Alvarado-García, César Cejudo-Castilla, Ivan Fernando Vilchis-Montalvo   +2 more
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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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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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Differentiation for Orders and Artinian Rings

Algebras and Representation Theory, 2004
Let \(R\) be a complete valuation domain. Given an \(R\)-order \(\Lambda\), we denote by \(\Lambda\text{-lat}\) the category of left \(\Lambda\)-lattices, that is, finitely generated left \(\Lambda\)-modules that are \(R\)-free. In his recent papers [J. Pure Appl. Algebra 153, No. 2, 171-190 (2000; Zbl 0964.16016) and Colloq. Math. 89, No.
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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
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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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The prüfer rings that are endomorphism rings of artinian modules

Communications in Algebra, 1994
In this paper we characterize the (commutative) Priifer rings that can be realized as endomorphism rings of artinian modules over arbitrary associative rings with identity (Theorem 4.7). This characterization is obtained by determining the structure of ∑-pure-injective modules over Prufer rings (Theorems 3.4 and 3.5)
CAMPS R, FACCHINI, ALBERTO
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Symmetrics in simple Artinian rings

1990
The authors prove four results about symmetric elements in simple Artinian rings with involution. Let R be a simple Artinian ring with involution *, char \(R\neq 2\), Z the center of R, and \(S=\{r\in R|\) \(r^*=r\}\). The four results assume that \(S\not\subset Z\) and that R is not \(M_ 2(GF(3))\) with symplectic involution, and are: (1) If \(\dim_ ...
Lee, Pjek-Hwee, Lee, Tsung-Cherng
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