• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.649-657
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• 2018

Let R be a commutative ring. In this paper, the w-projective Basis Lemma for w-projective modules is given. Then it is shown that for a domain, nonzero w-projective ideals and nonzero w-invertible ideals coincide. As an application, it is proved that R is a Krull domain if and only if every submodule of finitely generated projective modules is w-projective.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.273-277
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• 2003

The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then $A^{\ast}= X. In this paper, we show that if A is $\omega$-hyponormal and $B^{\ast}$ is invertible $\omega$-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then $A^{\ast}X = XB^{\ast}$.