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Abstract:
Let I be a monomial ideal of the polynomial ring S = K[x1,... ,x4] over a field K. Then S/I is sequentially Cohen-Macaulay if and only if S/I is pretty clean. In particular, if S/I is sequentially Cohen-Macaulay then I is a Stanley ideal.
Key Words: Monomial Ideals, Prime Filtrations, Pretty Clean Filtrations, Stanley Ideals.
2000 Mathematics Subject Classification: Primary: 13H10, Secondary: 13P10, 13C14, 13F20.
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