S. A. G. B. I. bases for rings of formal modular seminvariants (Q1281750)

The word SAGBI is an abbreviation of Subalgebra Analog to Gröbner bases for Ideals. SAGBI bases theory was introduced by \textit{L. Robbiano} and \textit{M. Sweedler} [in: Commutative algebra, Proc. Workshop, Salvador/Brazil 1988, Lect. Notes Math. 1430, 61-87 (1990; Zbl 0725.13013)] and independently by \textit{D. Kapur} and \textit{K. Madlener} [in: Computers and mathematics, Proc. Conf., Cambridge/Mass. 1989, 1-11 (1989; Zbl 0692.13001)]. The author constructs a SAGBI basis (and thus a generating set) of the ring of invariants for the four and five dimensional indecomposable modular representations of a cyclic group of prime order \(p\). It follows in particular that for the four dimensional representation the ring of invariants is generated in degree less than or equal to \(2p-3\), and for the five dimensional representation the ring of invariants is generated in degree less than or equal to \(2p-2\).