Mathematical Structures: History of Ore domains

# History of Ore domains

 Revision 2 . . July 31, 2004 10:45 pm by Jipsen Revision 1 . . July 10, 2004 10:45 am by Jipsen

Difference (from prior major revision) (no other diffs)

Changed: 28,30c28,29
 \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

Changed: 32c31
 \abbreviation{Abbr}
 \abbreviation{OreDom}

Changed: 35,38c34
 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}
 An Ore domain is a \href{Rings_with_identity.pdf}{ring with identity} $\mathbf{A}=\langle A,+,-,0,\cdot,1\rangle$ such that

Changed: 40c36
 $op_1$ is (name of property): $axiom_1$
 $\cdot$ is integral: $xy=0\implies x=0\text{ or }y=0$

Changed: 42c38
 $op_2$ is ...: $...$
 nonzero common multiples exist: $x\ne 0\ne y\implies\exists u\exists v(xu=yv\ne 0)\text{ and }\exists u\exists v(ux=vy\ne 0)$