대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권2호
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  • Pages.373-397
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A GENERALIZATION OF THE SYMMETRY PROPERTY OF A RING VIA ITS ENDOMORPHISM

  • 투고 : 2023.11.05
  • 심사 : 2024.01.26
  • 발행 : 2024.04.30
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초록

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.

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과제정보

The authors would like to thank the referee for careful reading.

참고문헌

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