scholarly journals Primary Decomposition of Lattice Basis Ideals

2000 ◽  
Vol 29 (4-5) ◽  
pp. 625-639 ◽  
Author(s):  
Serkan Hoşten ◽  
Jay Shapiro
Keyword(s):  
Primary Decomposition

On Stanley Depths of Certain Monomial Factor Algebras

2015 ◽  
Vol 58 (2) ◽  
pp. 393-401
Author(s):  
Zhongming Tang
Keyword(s):  
Polynomial Ring ◽  
Monomial Ideal ◽  
Primary Decomposition ◽  
Factor Algebra ◽  
Stanley Depth ◽  
Stanley Conjecture ◽  
Stanley Decomposition

AbstractLet S = K[x1 , . . . , xn] be the polynomial ring in n-variables over a ûeld K and I a monomial ideal of S. According to one standard primary decomposition of I, we get a Stanley decomposition of the monomial factor algebra S/I. Using this Stanley decomposition, one can estimate the Stanley depth of S/I. It is proved that sdepthS(S/I) ≤ sizeS(I). When I is squarefree and bigsizeS(I) ≤ 2, the Stanley conjecture holds for S/I, i.e., sdepthS(S/I) ≥ depthS(S/I).

The primary decomposition product of TKX-50 under adiabatic condition and its thermal decomposition

2018 ◽  
Vol 134 (3) ◽  
pp. 2049-2055 ◽  
Author(s):  
Junfeng Wang ◽  
Shusen Chen ◽  
Shaohua Jin ◽  
Rui Shi ◽  
Zhenfei Yu ◽  
...  
Keyword(s):  
Thermal Decomposition ◽  
Decomposition Product ◽  
Primary Decomposition ◽  
Adiabatic Condition

Primary decomposition of homogeneous ideal in idealization of a module

2018 ◽  
Vol 55 (3) ◽  
pp. 345-352
Author(s):  
Tran Nguyen An
Keyword(s):  
Noetherian Ring ◽  
Primary Decomposition ◽  
Associated Primes ◽  
Homogeneous Ideal ◽  
Finitely Generated ◽  
Commutative Noetherian Ring ◽  
Irreducible Decomposition

Let R be a commutative Noetherian ring, M a finitely generated R-module, I an ideal of R and N a submodule of M such that IM ⫅ N. In this paper, the primary decomposition and irreducible decomposition of ideal I × N in the idealization of module R ⋉ M are given. From theses we get the formula for associated primes of R ⋉ M and the index of irreducibility of 0R ⋉ M.

scholarly journals On the primary decomposition of some determinantal hyperedge ideal

2021 ◽  
Vol 103 ◽  
pp. 14-21
Author(s):  
Gerhard Pfister ◽  
Andreas Steenpaß
Keyword(s):  
Primary Decomposition
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