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12. Structure of zero-divisors to go up to related ideals.

Author

Jung, Da Woon, Lee, Chang Ik, Lee, Yang, and Piao, Zhelin

Subjects
*MATRIX rings, *POLYNOMIAL rings, *POLYNOMIALS, *RING theory
Abstract

AbstractThere are many ways for zero-dividing polynomials to go up to zero-dividing ideals when the base rings are IFP. The importance of these in ring theory leads us to consider the following ring conditions and study new useful roles of matrices for ring theory. Let R be a ring and a,b∈R\{0}. The first is the condition (*) that if ab = 0 then Ib = 0 for some nonzero ideal I⊆RaR of R or aJ = 0 for some nonzero ideal J⊆RbR of R. It is shown that from given any IFP ring, there can be constructed a non-IFP ring with the condition (*). We prove that a semiprime ring R with the condition (*) is both right and left nonsingular. The second is the condition (**) that if ab = 0 then IJ = 0 for some nonzero ideals I⊆RaR and J⊆RbR of R. We prove that every ring can be a subring of rings with the condition (**), that if R is an irreducible ring with the condition (**) then R is either a domain or non-semiprime, and that the condition (**) passes to polynomial rings when the base ring is semiprime. Various sorts of examples are given to illustrate and delimit the results obtained. [ABSTRACT FROM AUTHOR]

Published
2024
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29. Supplementary Table 1 from Cancer-Stimulated CAFs Enhance Monocyte Differentiation and Protumoral TAM Activation via IL6 and GM-CSF Secretion

Author

Cho, Haaglim, primary, Seo, Youngha, primary, Loke, Kin Man, primary, Kim, Seon-Wook, primary, Oh, Seong-Min, primary, Kim, Jun-Hyeong, primary, Soh, Jihee, primary, Kim, Hyoen Sik, primary, Lee, Hyunju, primary, Kim, Jin, primary, Min, Jung-Joon, primary, Jung, Da-Woon, primary, and Williams, Darren Reece, primary

Published
2023
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30. Supplementary Table 2 from Cancer-Stimulated CAFs Enhance Monocyte Differentiation and Protumoral TAM Activation via IL6 and GM-CSF Secretion

Author

Cho, Haaglim, primary, Seo, Youngha, primary, Loke, Kin Man, primary, Kim, Seon-Wook, primary, Oh, Seong-Min, primary, Kim, Jun-Hyeong, primary, Soh, Jihee, primary, Kim, Hyoen Sik, primary, Lee, Hyunju, primary, Kim, Jin, primary, Min, Jung-Joon, primary, Jung, Da-Woon, primary, and Williams, Darren Reece, primary

Published
2023
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31. Figure S1 to S22 from Cancer-Stimulated CAFs Enhance Monocyte Differentiation and Protumoral TAM Activation via IL6 and GM-CSF Secretion

Author

Cho, Haaglim, primary, Seo, Youngha, primary, Loke, Kin Man, primary, Kim, Seon-Wook, primary, Oh, Seong-Min, primary, Kim, Jun-Hyeong, primary, Soh, Jihee, primary, Kim, Hyoen Sik, primary, Lee, Hyunju, primary, Kim, Jin, primary, Min, Jung-Joon, primary, Jung, Da-Woon, primary, and Williams, Darren Reece, primary

Published
2023
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32. Supplementary Table 3 from Cancer-Stimulated CAFs Enhance Monocyte Differentiation and Protumoral TAM Activation via IL6 and GM-CSF Secretion

Author

Cho, Haaglim, primary, Seo, Youngha, primary, Loke, Kin Man, primary, Kim, Seon-Wook, primary, Oh, Seong-Min, primary, Kim, Jun-Hyeong, primary, Soh, Jihee, primary, Kim, Hyoen Sik, primary, Lee, Hyunju, primary, Kim, Jin, primary, Min, Jung-Joon, primary, Jung, Da-Woon, primary, and Williams, Darren Reece, primary

Published
2023
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