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Thoughts on Eggert's Conjecture
Eggert’s Conjecture Frobenius map on a finite-dimensional nilpotent commutative algebra finite abelian semigroup
2012/6/15
Eggert's Conjecture says that if R is a finite-dimensional nilpotent commutative algebra over a perfect field F of characteristic p, and R^{(p)} is the image of the p-th power map on R, then dim_F R \...
Stanley Conjecture on intersection of three monomial primary ideals
Monomial Ideals Stanley decompositions Stanley depth
2011/9/13
Abstract: We show that the Stanley's Conjecture holds for an intersection of three monomial primary ideals of a polynomial algebra S over a field.
On a Conjecture on the weak global dimension of Gaussian rings
Gaussian rings weak dimension content non-noetherian rings
2011/8/24
Abstract: Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is 0,1 or \infty. In this paper, we prove their conjecture in all cases except when R is a non-reduced local Gau...