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Algebra (416) 
SM ISO690:2012 DANCHEV, Peter. Commutative Weakly Tripotent Group Rings. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 2(93), pp. 2429. ISSN 10247696. 
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica  
Numărul 2(93) / 2020 / ISSN 10247696 /ISSNe 25874322  


CZU: 512.552  
MSC 2010: 16S34, 16U99, 20C07.  
Pag. 2429 



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Very recently, Breaz and Cˆımpean introduced and examined in Bull. Korean Math. Soc. (2018) the class of socalled weakly tripotent rings as those rings R whose elements satisfy at leat one of the equations x^{3} = x or (1 − x)^{3} = 1 − x. These rings are generally noncommutative. We here obtain a criterion when the commutative group ring RG is weakly tripotent in terms only of a ring R and of a group G plus their sections. Actually, we also show that these weakly tripotent rings are strongly invoclean rings in the sense of Danchev in Commun. Korean Math. Soc. (2017). Thereby, our established criterion somewhat strengthens previous results on commutative strongly invoclean group rings, proved by the present author in Univ. J. Math. & Math. Sci. (2018). Moreover, this criterion helps us to construct a commutative strongly invoclean ring of characteristic 2 which is not weakly tripotent, thus showing that these two ring classes are different. 

Cuvintecheie Tripotent rings, weakly tripotent rings, strongly invoclean rings, Group rings 


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