2023/03/01 by Neeraj Kumar, Kumar, Neeraj, Chitra Venugopal +1
Mathematics · #13-04 #13A02 #13A30 #13D02 #13P20 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2303.00350
openalex publication_date 2023/03/01 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28
Given a graded ring A and a homogeneous ideal I, the ideal is said to be of linear type if the Rees algebra of I is isomorphic to the symmetric algebra of I. In general, y-regularity of Rees algebra of I is 0 ⇒ I is generated by a d-sequence ⇒ I is of linear type. We show that d-sequence ideals represent a significantly smaller subset of ideals of linear type in terms of y-regularity. Moreover, we identify a class of d-sequences whose arbitrary powers generate ideals of Gröbner linear type. Notably, while d-sequences are inherently weak d-sequences, we highlight a specific class of algebras where weak d-sequences are indeed d-sequences.