« - Normal Lattices William
نویسنده
چکیده
An rj-normal lattice is a distributive lattice with 0 such that each prime ideal contains at most n minimal prime ideals. A relatively ra-normal lattice is a distributive lattice such that each bounded closed interval is an /¡.-normal lattice. The main results of this paper are: (1) a distributive lattice L with 0 is 71,-normal if and only if for any %n, x,,*•', X e L such that x Ax. = 0 for any i 4 j, i, / = 0, • • n,(xJ^(xirV.".W(xJ = L, l ' (2) a distributive lattice L is relatively n-normal if and only if for any n + l incomparable prime ideals P„, P., • •-, P , P.S/P. V ...VP = L. 77
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