Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

This research develops thermo-elastic analysis of a functionally graded cylinder under thermo-mechanical loadings. Heat conduction equation in cylindrical coordinate system is solved. Thermal conductivity coefficient is graded along the radial direction. By considering a symmetric distribution of temperature, loading and boundary conditions, strain-displacement and stress-strain relations can b...

Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses graded puts forward G(S5). Secondly, by employing operators that correspond operations in G(S5), we introduce concept of upper lower truth degrees a logical formula. Then, propose conditional degrees. Several basic interesting properties are addre...

We prove a completeness theorem for K:l, the infinitary extension of the graded version K O of the minimal normal logic K , allowing conjunctions and disjunctions of countable sets of formulas. This goal is achieved using both the usual tools of the normal logics with graded modalities and the machinery of the predicate infinitary logics in a version adapted to modal logic. Mathematics Subject ...

Let $R$ be a $G$-graded ring and M $R$-module. We define the graded primary spectrum of $M$, denoted by $\mathcal{PS}_G(M)$, to set all submodules $Q$ such that $(Gr_M(Q):_R M)=Gr((Q:_R M))$. In this paper, we topology on $\mathcal{PS}_G(M)$ having Zariski prime $Spec_G(M)$ as subspace topology, investigate several topological properties space.

Let A be a Z-graded associative algebra and let ρ be an irreducible N-graded representation of A on W with finite-dimensional homogeneous subspaces. Then it is proved that ρ(Ã) = glJ (W ), where à is the completion of A with respect to a certain topology and glJ (W ) is the subalgebra of EndW , generated by homogeneous endomorphisms. It is also proved that an N-graded vector space W with finite...