a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

Background and Aim: One of the key aspects of maternal care is observing the progress of labor. Careful assessment of labor progress could provide mothers to be referred on time and could decrease the maternal and neonatal morbidity. This study aimed to compare diagnostic accuracy of purple line with transvers diagonal of Michaelis sacral rhomboid to predict labor progress in nulliparous and mu...

We show that any pointed, peordered module map BFgr(E)→BFgr(F) between Bowen-Franks modules of finite graphs can be lifted to a unital, graded, diagonal preserving ⁎-homomorphism Lℓ(E)→Lℓ(F) the corresponding Leavitt path algebras over commutative unital ring with involution ℓ. Specializing case when ℓ is field, we establish fullness part Hazrat's conjecture about functor from ℓ-algebras preord...

Within a constructive homological algebra approach, we study the factorization and decomposition problems for a class of linear functional (determined, over-determined, under-determined) systems. Using the concept of Ore algebras of functional operators (e.g., ordinary/partial differential operators, shift operators, time-delay operators), we first concentrate on the computation of morphisms fr...

abstract. let (r,p) be a noetherian unique factorization do-main (ufd) and m be a finitely generated r-module. let i(m)be the first nonzero fitting ideal of m and the order of m, denotedord_r(m), be the largest integer n such that i(m) ⊆ p^n. in thispaper, we show that if m is a module of order one, then either mis isomorphic with direct sum of a free module and a cyclic moduleor m is isomorphi...