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\Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} % Note: replace "Template" with Name_of_class in previous line |
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\Large Ore domains \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Ore_domains}{edit} |
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\abbreviation{Abbr} |
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\abbreviation{OreDom} |
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A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that $\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class} |
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An Ore domain is a \href{Rings_with_identity.pdf}{ring with identity} $\mathbf{A}=\langle A,+,-,0,\cdot,1\rangle$ such that |
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$op_1$ is (name of property): $axiom_1$ |
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$\cdot$ is integral: $xy=0\implies x=0\text{ or }y=0$ |
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$op_2$ is ...: $...$ |
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nonzero common multiples exist: $x\ne 0\ne y\implies\exists u\exists v(xu=yv\ne 0)\text{ and }\exists u\exists v(ux=vy\ne 0)$ |
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