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Linear strand of edge ideals of comaximal graphs of commutative rings.
- Source :
- Communications in Algebra; 2024, Vol. 52 Issue 4, p1486-1500, 15p
- Publication Year :
- 2024
-
Abstract
- For an edge ideal I(G) of a simple graph G , we study the N -graded Betti numbers that appear in the linear strand of the minimal free resolution of I (Γ (Z n)) , where Γ (Z n) is the comaximal graph of the integral modulo ring Z n . We show that the extremal Betti number of I (Γ (Z n)) is ϕ (n) , where ϕ (n) is the Euler's totient function and thereby we obtain a large class of edge ideals with even extremal Betti numbers. We find the regularity (Castelnuovo-Mumford) and the projective dimension of these ideals. Moreover, we exhibit explicit formulae that determine all the N -graded Betti numbers in the linear strand of the minimal free resolution of I (Γ (Z n)) for certain values of n. [ABSTRACT FROM AUTHOR]
- Subjects :
- BETTI numbers
COMMUTATIVE rings
MODULES (Algebra)
RINGS of integers
Subjects
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 52
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 175911804
- Full Text :
- https://doi.org/10.1080/00927872.2023.2263559