2020/10/22 by Herzog, Jürgen, Hibi, Takayuki, Moradi, Somayeh · 2 citations
#05E40 #13A02 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2010.11516
Let S=K[x1,…,xn] be the polynomial ring over a field and A a standard graded S-algebra. In terms of the Gröbner basis of the defining ideal J of A we give a condition, called the x-condition, which implies that all graded components Ak of A have linear quotients and with additional assumptions are componentwise linear. A typical example of such an algebra is the Rees ring R(I) of a graded ideal or the symmetric algebra Sym(M) of a module M. We apply our criterion to study certain symmetric algebras and the powers of vertex cover ideals of certain classes of graphs.