objective: hla-g is a nonclassical major histocompatibility complex antigen and is expressed as seven isoforms, including four membrane bound (hla-g1 to –g4) and three soluble (hla-g5 to –g7) forms. the pattern of selective expression of hla-g transcripts in tissues shows the existence of a tight transcriptional control on the gene expression. it has been revealed that cytokines including inter...

In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.

Máıra Aguiar, Nico Stollenwerk and Bob W. Kooi Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Avenida Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal; Instituto Gulbenkian de Ciência, Apartado 14, 2781-901 Oeiras, Portugal ; Faculty of Earth and Life Sciences, Department of Theoretical Biology, Vrije Universiteit Amsterdam, De Boelelaan 1087, NL 1081 HV Amsterdam, The Net...

The two classical hard problems underlying the security of lattice-based cryptography are the shortest vector problem (SVP) and the closest vector problem (CVP). For SVP, lattice sieving currently has the best (heuristic) asymptotic time complexity: in high dimensions d, sieving can solve SVP in time 2, using 2 memory [Becker– Ducas–Gama–Laarhoven, SODA’16]. The best heuristic time complexity t...

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties.  Moreover, we give conditions  ...

 Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

the aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered ag-groupoids with left identity. these concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered ag-groupoids, so it seems to be interesting to study them.

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.