We consider a ring R = K[∂; id, θ] of differential operators over a differential field (K, θ). This is a (left and right) principal ideal domain. Hence, if R is simple, then for every matrix M ∈ R n n there exist unimodular matrices S and T ∈ R n n and f ∈ R such that SMT = diag(1, . . . , 1, f, 0, . . . , 0). The proof of the existence goes back to Jacobson, Nakayama and Teichmüller. Therefore...

We study the surface S̄ parametrizing cuboids: it is defined by the equations relating the sides, face diagonals and long diagonal of a rectangular box. It is an open problem whether a ‘rational box’ exists, i.e., a rectangular box all of whose sides, face diagonals and long diagonal have (positive) rational length. The question is equivalent to the existence of nontrivial rational points on S̄. ...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

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...

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

let $r$ be a commutative ring. in this paper we assert some properties of finitely generated comultiplication modules and fitting ideals of them.

we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. In this paper we give some constructions of pairwise orthogonal diagonal Latin squares. As an application of such constructions we obtain some new infinite classes of pairwise orthogonal diagonal Latin squares which are useful in the study of pairwise orthogonal diagonal Latin squares.