Triangular matrix coalgebras and applications

Differential Polynomial Rings of Triangular Matrix Rings

Strongly clean triangular matrix rings with endomorphisms

‎A ring $R$ is strongly clean provided that every element‎ ‎in $R$ is the sum of an idempotent and a unit that commutate‎. ‎Let‎ ‎$T_n(R,sigma)$ be the skew triangular matrix ring over a local‎ ‎ring $R$ where $sigma$ is an endomorphism of $R$‎. ‎We show that‎ ‎$T_2(R,sigma)$ is strongly clean if and only if for any $ain‎ ‎1+J(R)‎, ‎bin J(R)$‎, ‎$l_a-r_{sigma(b)}‎: ‎Rto R$ is surjective‎. ‎Furt...

Localization in Coalgebras. Applications to Finiteness Conditions

Let k be a field. Given two finite-dimensional right comodules N andM over a k–coalgebra C, the k–vector spaces ExtC(N,M) need not to be finite-dimensional. This is due to the fact that the injective right comodules appearing in the minimal injective resolution of M need not to be of finite dimension or even quasi-finite. The obstruction here is that factor comodules of quasi-finite comodules a...

On Skew Triangular Matrix Rings

For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring Tn(R,α). By using an ideal theory of a skew triangular matrix ring Tn(R,α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x;α]/〈xn〉, for each positive integer n, where R[x;α] is the skew polynomial ring, and 〈xn〉 is the ideal generated by xn.

Extended Triangular Operational Matrix For Solving Fractional Population Growth Model

  In this paper, we apply the extended triangular operational matrices of fractional order to solve the fractional voltrra model for population growth of a species in a closed system. The fractional derivative is considered in the Caputo sense. This technique is based on generalized operational matrix of triangular functions. The introduced method reduces the proposed problem for solving a syst...