On The Properties of Idempotents of the Matrix Ring M3 (zn[x])

Gaurav Mittal; Kanika Singla

doi:https://doi.org/10.14445/22315373/IJMTT-V53P531

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 4 | Year 2018 | Article Id. IJMTT-V53P531 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P531

On The Properties of Idempotents of the Matrix Ring M3 (zn[x])

Gaurav Mittal, Kanika Singla

Abstract

In this paper, we find all the idempotents of 3×3 upper (lower) triangular matrices over the commutative ring Z_p, i.e., U₃(Z_p[x]) (L₃(Z_p[x])) for any prime p. We also show that for the ring of upper (lower) triangular matrices over Z_n[x], i.e., U₃(Z_n[x]) (L₃(Z_n[x])), every diagonal entry of any idempotent matrix in U₃(Z_n[x]) (L₃(Z_n[x])) must be an idempotent of Z_n for every n.

Keywords

Idempotents, Upper triangular matrices, Lower triangular matrices, Commuta- tive rings, Polynomial Rings.

References

[1] Idempotents and units of matrix rings over polynomial rings, Pramod Kanwar, Meenu Khatkar and R. K. Sharma, International Electronic Journal of Algebra Volume 22 (2017) 147 - 169.
[2] Idempotents in ring extensions, P. Kanwar, A. Leroy and J. Matczuk, J. Algebra, 389 (2013), 128 - 136.

Citation :

Gaurav Mittal, Kanika Singla, "On The Properties of Idempotents of the Matrix Ring M3 (zn[x])," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 4, pp. 254-258, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P531