Is There an Ideal Membership Size?

2018 ◽  
Vol 14 (9) ◽  
pp. 4-4
Keyword(s):  
Ideal Membership

scholarly journals Univariate Ideal Membership Parameterized by Rank, Degree, and Number of Generators

2021 ◽  
Author(s):  
V. Arvind ◽  
Abhranil Chatterjee ◽  
Rajit Datta ◽  
Partha Mukhopadhyay
Keyword(s):  
Number Of Generators ◽  
Ideal Membership

scholarly journals Local zero estimates and effective division in rings of algebraic power series

2018 ◽  
Vol 2018 (737) ◽  
pp. 111-160 ◽  
Author(s):  
Guillaume Rond
Keyword(s):  
Power Series ◽  
Necessary Condition ◽  
Effective Solution ◽  
Gap Theorem ◽  
Division Theorem ◽  
Ideal Membership ◽  
Formal Power ◽  
Algebraic Power Series ◽  
Ideal Membership Problem ◽  
The Ideal

AbstractWe give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact, we show that this condition is also sufficient when the module is a ring with some additional properties. To prove this result we show an effective Weierstrass Division Theorem and an effective solution to the Ideal Membership Problem in rings of algebraic power series. Finally, we apply these results to prove a gap theorem for power series which are remainders of the Grauert–Hironaka–Galligo Division Theorem.

scholarly journals Ideal membership in signomial rings

2007 ◽  
pp. 64-67
Author(s):  
Zarko Mijajlovic ◽  
Milos Milosevic ◽  
Aleksandar Perovic
Keyword(s):  
Finitely Generated ◽  
Ideal Membership

The paper presents decidability of ideal membership for finitely generated signomial ideals with rational exponents over computable field K of characteristic 0. We also prove the existence of no-recursive ideals in K[xQ], where xQ = xQ1?.xQn n is a multiplicative copy of the monoid Qn = Q ( ? ( Q.

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