• Title/Summary/Keyword: qb-ideal

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ON EXCHANGE qb-IDEALS

  • CHEN, HUANYIN;CHEN, MIAOSEN
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.45-51
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    • 2005
  • In this paper, we establish necessary and sufficient conditions for an exchange ideal to be a qb-ideal. It is shown that an exchange ideal I of a ring R is a qb-ideal if and only if when-ever $a{\simeq}b$ via I, there exists u ${\in} I_q^{-1}$ such that a = $ubu_q^{-1}$ and b = $u_q^{-1}$. This gives a generalization of the corresponding result of exchange QB-rings.

ON QB-IDEALS OF EXCHANGE RINGS

  • Chen, Huanyin
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.873-884
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    • 2009
  • We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.

A GENERALIZATION OF THE SYMMETRY PROPERTY OF A RING VIA ITS ENDOMORPHISM

  • Fatma Kaynarca;Halise Melis Tekin Akcin
    • Communications of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.373-397
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    • 2024
  • Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly α-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring R as strongly α-symmetric if the skew polynomial ring R[x; α] is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly α-symmetric rings.