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In this work, we consider the finite ring F_2 +uF_2 +vF_2, u^2 = 1;v^2 = 0, u.v = v.u = 0 which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes over F_2+uF_2+vF_2 of odd length. These codes are compared with codes that had priorly been obtained on the finite field F_2. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over F_2+uF_2+vF_2 of odd length n is a quasicyclic code of index 4 with length 4n over F_2. In particular, the Gray images are applied to two different rings S_1 = F_2+vF_2, v^2 = 0 and S_2 = F_2+uF_2, u^2 = 1 and negacyclic and constacyclic images of these rings are also discussed.

A module M is called principally Goldie*-lifting if for every proper cyclic submodule X of M, there is a direct summand D of M such that Xβ

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One of the generalizations of supplemented modules is the Goldie*-supplemented module, defined by Birkenmeier et al. using $\beta^{\ast}$ relation. In this work, we deal with the concept of the cofinitely Goldie*-supplemented modules as a version of Goldie*-supplemented module. A left $R$-module $M$ is called a cofinitely Goldie*-supplemented module if there is a supplement submodule $S$ of $M$ with $C\beta^{\ast}S$, for each cofinite submodule $C$ of $M$. Evidently, Goldie*-supplemented are cofinitely Goldie*-supplemented. Further, if $M$ is cofinitely Goldie*-supplemented, then $M/C$ is cofinitely Goldie*-supplemented, for any submodule $C$ of $M$. If $A$ and $B$ are cofinitely Goldie*-supplemented with $M=A\oplus B$, then $M$ is cofinitely Goldie*-supplemented. Additionally, we investigate some properties of the cofinitely Goldie*-supplemented module and compare this module with supplemented and Goldie*-supplemented modules.