The characterization problem for endomorphism rings

Garcia, J. G.

doi:10.1017/s1446788700032602

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Theorem 7 For Every Ring R1

Notation and Preliminaries1

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1993

1999

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Cited by 6 publications

(2 citation statements)

References 18 publications

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“…Then there exists α : I → I such that α = α • f 1 . By [5],ᾱ is the right multiplication by some a ∈ E. It is clear that a ∈ f 1 J and hence δ(a) ∈ f 1 B. Therefore, δ(a) = δ(a) finite f j and hence a = a finite f j .…”

Section: Theorem 7 For Every Ring Rmentioning

confidence: 99%

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Isomorphisms of row and column finite matrix rings

Haefner

Río²,

Simón³

1997

Proc. Amer. Math. Soc.

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Abstract. This paper investigates the ring-theoretic similarities and the categorical dissimilarities between the ring RF M (R) of row finite matrices and the ring RCF M (R) of row and column finite matrices. For example, we prove that two rings R and S are Morita equivalent if and only if the rings RCF M (R) and RCF M (S) are isomorphic. This resembles the result of V. P. Camillo (1984) for RF M (R). We also show that the Picard groups of RF M (R) and RCF M (R) are isomorphic, even though the rings RF M (R) and RCF M (R) are never Morita equivalent.

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Section: Theorem 7 For Every Ring Rmentioning

confidence: 99%

“…Actually, RCF M (R) is the idealizer of F M(R) in RF M (R). F M(R) is the right ideal of RF M (R) generated by {e i | i ∈ N} (see [5]). Moreover,…”

Section: Notation and Preliminariesmentioning

confidence: 99%