A Steenrod-Milnor action ordering on Dickson invariants
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Let A be the Steenrod algebra and D(V ) the Dickson algebra. An ordering in D(V ) is defined according to the Steenrod algebra action. Using this ordering, we prove the following: Let f 2 EndA (D(V )) be an A-linear degree preserving map. If f is non-zero on the lowest degree, then f is an isomorphism. Moreover, EndA D(V ) is a local ring, where D(V ) is its augmentation ideal.
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Dickson algebra, Steenrod algebra, Isomorphisms of, Dickson algebras, Local rings.
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Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών