ABSTRACT
Stanley-Reîsner rings and affine semigroup rings are very important subjects of modern commutative algebra (c.f. https://www.w3.org/1998/Math/MathML"> [ 4,22 ] ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175633/5bc16269-a792-4117-a208-ca03c55a3a8d/content/eq5966.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . For the study of these https://www.w3.org/1998/Math/MathML"> Z n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175633/5bc16269-a792-4117-a208-ca03c55a3a8d/content/eq5967.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -graded rings, combinatorial descriptions of the local cohomology modules with supports in graded maximal ideals have been a fundamental tool. But recently, local cohomology modules with supports in general https://www.w3.org/1998/Math/MathML"> Z n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175633/5bc16269-a792-4117-a208-ca03c55a3a8d/content/eq5968.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -graded ideals (i.e., monomial ideals) are investigated by several authors (c.f. https://www.w3.org/1998/Math/MathML"> [ 1,10 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175633/5bc16269-a792-4117-a208-ca03c55a3a8d/content/eq5969.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , https://www.w3.org/1998/Math/MathML"> 17,18,19,20,21,25,26,27 ] ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175633/5bc16269-a792-4117-a208-ca03c55a3a8d/content/eq5970.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . It might extend the framework of the theory of the https://www.w3.org/1998/Math/MathML"> Z n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429175633/5bc16269-a792-4117-a208-ca03c55a3a8d/content/eq5971.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -graded rings and modules.
