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المقاله
1 - A note on the new basis in the mod 2 Steenrod algebraJournal of Linear and Topological Algebra , العدد 2 , السنة 7 , بهار 2018The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations, denoted by $Sq^n$, between the cohomology groups with $\mathbb{Z}_2$ coefficients of any topological space. Regarding to its vector spac أکثرThe Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations, denoted by $Sq^n$, between the cohomology groups with $\mathbb{Z}_2$ coefficients of any topological space. Regarding to its vector space structure over $\mathbb{Z}_2$, it has many base systems and some of the base systems can also be restricted to its sub algebras. On the contrary, in addition to the work of Wood, in this paper we define a new base system for the Hopf subalgebras $\mathcal{A}(n)$ of the mod $2$ Steenrod algebra which can be extended to the entire algebra. The new base system is obtained by defining a new linear ordering on the pairs $(s+t,s)$ of exponents of the atomic squares $Sq^{2^s(2^t-1)}$ for the integers $s\geq 0$ and $t\geq 1$. تفاصيل المقالة -
المقاله
2 - Digital cohomology groups of certain minimal surfacesJournal of Linear and Topological Algebra , العدد 5 , السنة 7 , پاییز 2018In this study, we compute simplicial cohomology groups with different coefficientsof a connected sum of certain minimal simple surfaces by using the universal coefficienttheorem for cohomology groups. The method used in this paper is a different way to computedigital co أکثرIn this study, we compute simplicial cohomology groups with different coefficientsof a connected sum of certain minimal simple surfaces by using the universal coefficienttheorem for cohomology groups. The method used in this paper is a different way to computedigital cohomology groups of minimal simple surfaces. We also prove some theorems relatedto degree properties of a map on digital spheres. تفاصيل المقالة -
المقاله
3 - Invariant elements in the dual Steenrod algebraJournal of Linear and Topological Algebra , العدد 4 , السنة 8 , تابستان 2019In this paper, we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${\mathcal{A}_p}^*$ under the conjugation map $\chi$ and give bounds on the dimensions of $(\chi-1)({\mathcal{A}_p}^*)_d$, where $({\mathcal{A}_p}^*)_d$ أکثرIn this paper, we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${\mathcal{A}_p}^*$ under the conjugation map $\chi$ and give bounds on the dimensions of $(\chi-1)({\mathcal{A}_p}^*)_d$, where $({\mathcal{A}_p}^*)_d$ is the dimension of ${\mathcal{A}_p}^*$ in degree $d$. تفاصيل المقالة -
المقاله
4 - Conjectures on the anti-automorphism of Z-basis of the Steenrod algebraJournal of Linear and Topological Algebra , العدد 1 , السنة 10 , زمستان 2021In this paper, we compute the images of some of the $Z$-basis elements under the anti-automorphism map $\chi$ of the mod 2 Steenrod algebra $\mathcal{A}_2$ and propose some conjectures based on our computations.In this paper, we compute the images of some of the $Z$-basis elements under the anti-automorphism map $\chi$ of the mod 2 Steenrod algebra $\mathcal{A}_2$ and propose some conjectures based on our computations. تفاصيل المقالة