Nilary group rings and algebras
نویسندگان
چکیده
A ring $A$ is (principally) nilary, denoted (pr-)nilary, if whenever $XY=0,$ then there exists a positive integer $n$ such that either $X^n=0$ or $Y^n=0$ for all (principal) ideals $X$, $Y$ of $A$. We determine necessary and/or sufficient conditions the group $A[G]$ to be nilary in terms on $G$. For example, we show that: (1) If (pr-)nilary and $G$ prime order each finite nontrivial normal subgroup nilpotent (2) Assume finite. Then only $p$-group, $char(A)=p^\alpha $ ($p$ prime), (pr-)nilary. (3) Let supersolvable $q$ smallest dividing G ,$ $F$ field with $char(F)=q$. $F[G]$ $q$-group. Examples are provided illustrate delimit our results.
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ژورنال
عنوان ژورنال: Turkish Journal of Mathematics
سال: 2023
ISSN: ['1303-6149', '1300-0098']
DOI: https://doi.org/10.55730/1300-0098.3412