In this paper, we introduce and study graded 2-absorbing and graded weakly 2-absorbing ideals of a graded ring which are different from 2-absorbing and weakly 2-absorbing ideals. We give some properties and characterizations of these ideals and their homogeneous components. We investigate graded (weakly) 2-absorbing ideals of R1 × R2 where R1 and R2 are two graded rings.

Vincristine (VCR), vinblastine (VBL) and vinorelbine (VRL) are anticancer agents from the Vinca alkaloid family that have the potential to induce genotoxic effect. The aim of the present study was to compare the genotoxic effect of VCR, VBL and VRL. Levels of 8-hydroxy-2-deoxy guanosine (8-OHdG) and sister chromatid exchanges (SCEs) were measured in cultured human blood lymphocytes treated with VCR, VBL and VRL at concentrations of 0.01 and 0.1 μg/mL. Results showed that VCR, VBL and VRL significantly increased the 8-OHdG levels (p <0.05), whereas it did not cause a significant increase in the frequencies of SCEs in human blood lymphocytes as compared to controls. On the other hand, all three agents significantly increased cells mitotic index (p <0.05). At both tested concentrations, the magnitude of the increase in 8-OHdG was VBL>VCR>VRL. In conclusion, VCR, VBL and VRL induce DNA damage as indicated by the increase in the 8-OHdG biomarker but with different magnitude.

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded 2-absorbing and graded weakly 2-absorbing submodules of a graded modules over a commutative graded ring.

Abstract. Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study graded 2-absorbing primary and graded weakly 2-absorbing primary ideals of a graded ring which are different from 2-absorbing primary and weakly 2-absorbing primary ideals. We give some properties and characterizations of these ideals and their homogeneous components.

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