Further results on skew monoid rings of a certain free monoid (I)

K Paykan,M Habibi,Nigel Byott

doi:10.1080/23311835.2018.1436664

K Paykan, M Habibi + Show 1 more

Open Access

https://doi.org/10.1080/23311835.2018.1436664

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Abstract

Let R be a ring with an endomorphism , F be a free monoid and S be a factor of such that for some positive integer . The second author and Moussavi [Annihilator properties of skew monoid rings, Com...

Highlights

Throughout this article, all rings are associative with identity, and 1 will always stand for the identity of the monoid S and the ring R
We show how the aforementioned classical ring constructions can be viewed as special cases of the skew monoid ring construction of a certain free monoid
Example 2.3 Let R be a ring with an endomorphism, and let S be a free monoid generated by = {u, v} with 0 added and the relation u2 = v3 = vu = 0

Summary

Introduction

Throughout this article, all rings are associative with identity, and 1 will always stand for the identity of the monoid S and the ring R. For a ring R, we denote by U(R) and J(R) the set of invertible elements and the Jacobson radical of R, respectively. For a non-empty subset X ⊂ R, rR(X) and R(X) denote the right and left annihilators of X in R, respectively. Z (R) and Zr(R) denote the left and right singular ideals of R, respectively. Let R be a ring with an endomorphism with (1) = 1. Is a ring with usual addition and multiplication subject to the relation uir = (r)ui, ABOUT THE AUTHORS. Kamal Paykan is an Assistant professor of Mathematics in the Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran. Mohammad Habibi is an Assistant professor of Mathematics in the Department of Mathematics, Tafresh University, Tafresh, Iran. The authors have completed their PhD course from Tarbiat Modares University under the guidance of Moussavi

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Now assume

Proof Suppose that