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.  

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...

We give a crystal-theoretic proof that nonsymmetric Macdonald polynomials specialized to t=0 are affine Demazure characters. explicitly construct an crystal on semistandard key tabloids such removing the edges recovers finite crystals constructed earlier by authors. also realize filtration highest weight modules defining explicit embedding operators which, at level of characters, parallels recu...

In the present paper we study representations of Jacobi algebra. More concretely, define, analogously to case semi-simple Lie algebras, Verma modules over algebra ${\cal G}_2$. We their reducibility and give explicit construction reducible exhibiting corresponding singular vectors. Using this information a complete classification modules. than exhibit interrelation embeddings between these Thes...

Histological subtype of papillary (p) renal cellular and cell-layer level patterns almost cannot be captured by existing CNN-based models in large-size histopathological images, which brings obstacles to directly applying these such a fine-grained classification task. This paper proposes novel instance-based Vision Transformer (i-ViT) learn robust representations images for the pRCC subtyping t...

Although significant progress has been achieved recently in automatic learning of steganographic cost, the existing methods designed for spatial images cannot be directly applied to JPEG which are more common media daily life. The difficulties migration mainly caused by characteristics <te...

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.