On the lifting problem for homogeneous ideals

Lifting Problem in Codimension 2 and Initial Ideals

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

lifting problem in codimension 2 and initial ideals

Lifting Chains of Prime Ideals

We give an elementary proof that for a ring homomorphism A → B satisfying the property that every ideal in A is contracted from B the following property holds: for every chain of prime ideals p0 ⊂ . . . ⊂ pr in A there exists a chain of prime ideals q0 ⊂ . . . ⊂ qr in B such that qi ∩ A = pi. Mathematical Subject Classification (1991): 13B24. Let A and B be commutative rings and let φ : A → B b...

Initial Ideals of Truncated Homogeneous Ideals

Denote by R the power series ring in countably many variables over a eld K; then R 0 is the smallest sub-algebra of R that contains all homogeneous elements. It is a fact that a homogeneous, nitely generated ideal J in R 0 have an initial ideal gr(J), with respect to an arbitrary admissible order, that is locally nitely generated in the sense that dimK gr(J) d P d?1 j=1 R 0 j gr(J) d?j < 1 for ...