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Atoms in Quasilocal Integral Domains. (arXiv:1810.02922v1 [math.AC])
来源于:arXiv
Let $(R,M)$ be a quasilocal integral domain. We investigate the set of
irreducible elements (atoms) of $R$. Special attention is given to the set of
atoms in $M \backslash M^2$ and to the existence of atoms in $M^2$. While our
main interest is in local Cohen-Kaplansky (CK) domains (atomic integral domains
with only finitely many non-associate atoms), we endeavor to obtain results in
the greatest generality possible. In contradiction to a statement of Cohen and
Kaplansky, we construct a local CK domain with precisely eight nonassociate
atoms having an atom in $M^2$. 查看全文>>