Document Type: Research Paper


Department of Mathematics‎, ‎Faculty of Arts and Sciences‎, ‎Eastern Mediterranean University‎, ‎Famagusta‎, ‎North Cyprus Via Mersin 10‎, ‎Turkey


‎Let $\mathcal{A}_p$ be the mod $p$ Steenrod algebra‎, ‎where $p$ is an odd prime‎, ‎and let $\mathcal{A}$ be the‎ subalgebra $\mathcal{A}$ of $\mathcal{A}_p$ generated by the Steenrod $p$th powers‎. ‎We generalize the $X$-basis in $\mathcal{A}$ to $\mathcal{A}_p$‎.


Main Subjects

[1] D. Arnon, Monomial bases in the Steenrod algebra, J. Pure. Appl. Algebra. 96 (1994), 215-223.

[2] D. Yu. Emelyanov, Th. Yu. Popelensky, On monomial bases in the mod-p Steenrod algebra, J. Fixed Point Theory Appl. 17 (2) (2015), 341-353.

[3] I. Karaca, Monomial bases in the mod-p Steenrod algebra. Czech. Math. J. 55 (3) (2005), 699-707.

[4] J. Milnor, The Steenrod algebra and its dual, Ann. Math. 67 (1958), 150-171.

[5] S. Papastavridis, Generators and relations in the mod p Steenrod algebra, Stud. Algebr. Topol. Adv. Math. Suppl. 5 (1979), 167-188.

[6] N. E. Steenrod, Cohomology Operations, Annals of Math Studies 50 Princeton University Press, 1962.

[7] N. D. Turgay, I. Karaca, The Arnon bases in the Steenrod algebra, Georgian. Math. J. (2018), DOI:10.1515/gmj-2018-0076.

[8] C. T. C. Wall, Generators and relations for the Steenrod algebra, Ann. Math. 72 (1960), 429-444.

[9] R. M. W. Wood, Problems in the Steenrod algebra, Bull. London Math. Soc. 30 (5) (1998), 449-517.