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A solution of Eggert's conjecture in special clases
김세경,박종률 호남수학회 2005 호남수학학술지 Vol.27 No.3
Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let Mp be the sub-algebra of M generated by xp,x ∈ M. Eggert[3] conjectures that dimkM ≥ pdimkMp.In this paper, we show that the conjecture holds for M = R+/I, where R = k[X1,X2, ,Xt] is a polynomial ring with indetermi nates X1,X2, ,Xt over k and R+ is the maximal ideal of R generated by X1,X2, ,Xt and I is a monomial ideal of R con taining X1 n1+1,X2 n2+1 , ,Xtnt+1 (ni ≥ 0 for all i).