a subgroup $h$ is said to be $s$-permutable in a group $g$‎, ‎if‎ ‎$hp=ph$ holds for every sylow subgroup $p$ of $g$‎. ‎if there exists a‎ ‎subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every‎ ‎sylow subgroup of $b$‎, ‎then $h$ is said to be $ss$-quasinormal in‎ ‎$g$‎. ‎in this paper‎, ‎we say that $h$ is a weakly $ss$-quasinormal‎ ‎subgroup of $g$‎, ‎if there is a normal subgroup ...

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study weakly prime ideals. We investigate rings in which all graded...

In this paper we have generalized the concepts of   q   , -fuzzy ideals,   q   , -fuzzy quasi-ideals and   q   , -fuzzy bi-ideals by introducing the concepts of   k q   , -fuzzy ideals,   k q   , -fuzzy quasiideals and   k q   , -fuzzy bi-ideals in ternary semigroups and several related properties are investigated. Different characterizations of regular and weakly ...

Our initial problem is to represent classes $$m$$ modulo $$q$$ by a sum of three terms, two being taken from rather small sets $$\mathcal A$$ and B$$ the third one having an odd number prime factors (the so-called irregular numbers in S. Ramanujan’s terminology) lying interval $$[q^{20r},q^{20r}+q^{16r}]$$ for some given $$r\ge1$$ . We show that it always possible do so provided $$|\mathcal A|\...