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.

‎let $g$ be a group with identity $e.$ let $r$ be a $g$-graded‎ ‎commutative ring and $m$ a graded $r$-module‎. ‎in this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎for example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $m$ are studied‎.‎

let  be a graded ring and  be a graded -module. we define a topology on graded prime spectrum  of the graded -module  which is analogous to that for , and investigate several properties of the topology.

The Extra cortical Clamp Device (ECD) is a novel fixation element designed for use in external fixation assemblies. Unlike standard transosseous fixation elements such as fine wires or the Schanz screw, the ECD avoids the intramedullary canal by obtaining capture of the bone segment external to the periosteal surface of diaphyseal bone. The prime advantage of this is to avoid disruption of, and...

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

The N-glycosidic bond can be hydrolyzed spontaneously or by glycosylases during removal of damaged bases by the base excision repair pathway, leading to the formation of highly mutagenic apurinic/apyrimidinic (AP) sites. Organisms encode for evolutionarily conserved repair machinery, including specific AP endonucleases that cleave the DNA backbone 5' to the AP site to prime further DNA repair s...

Effects of incision angle in construction of clear corneal cataract incision are studied with optical coherence tomography (OCT). A stable incision angle range is found to be existent for single-planed, clear corneal cataract incisions. When well pressurized, incision angles within this stable range result in well-apposed incision edges that resist gapping while incision angles falling outside ...

Let $R$ be a commutative ring with identity‎. ‎A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$‎, ‎$a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...

BACKGROUND Guarding pain after rat plantar incision is similar to pain at rest in postoperative patients. Spontaneous activity (SA) in nociceptive pathways quite likely transmits such ongoing pain. This study examined the extent of tissue injury by incision on pain behaviors and nociceptor SA. METHODS Rat pain behaviors were measured after a sham procedure, skin incision, or skin plus deep ti...