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FULLY PRIME MODULES AND FULLY SEMIPRIME MODULES
Beachy, John A.,Medina-Barcenas, Mauricio Korean Mathematical Society 2020 대한수학회보 Vol.57 No.5
Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module M, we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by M. We also consider the relationship between the conditions (1) M is a fully prime (semiprime) module, and (2) the endomorphism ring of M is a fully prime (semiprime) ring.
PRIME M-IDEALS, M-PRIME SUBMODULES, M-PRIME RADICAL AND M-BAER'S LOWER NILRADICAL OF MODULES
Beachy, John A.,Behboodi, Mahmood,Yazdi, Faezeh Korean Mathematical Society 2013 대한수학회지 Vol.50 No.6
Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, it coincides with prime (resp. semiprime) submodule of X. Other concepts encountered in the general theory are M-$m$-system sets, M-$n$-system sets, M-prime radical and M-Baer's lower nilradical of modules. Relationships between these concepts and basic properties are established. In particular, we identify certain submodules of M, called "primeM-ideals", that play a role analogous to that of prime (two-sided) ideals in the ring R. Using this definition, we show that if M satisfies condition H (defined later) and $Hom_R(M,X){\neq}0$ for all modules X in the category ${\sigma}[M]$, then there is a one-to-one correspondence between isomorphism classes of indecomposable M-injective modules in ${\sigma}[M]$ and prime M-ideals of M. Also, we investigate the prime M-ideals, M-prime submodules and M-prime radical of Artinian modules.
Prime M-ideals, M-prime submodules, M-prime radical and M-Baer's lower nilradical of modules
John Beachy,Mahmood Behboodi,Fayezeh Yazdi 대한수학회 2013 대한수학회지 Vol.50 No.6
Let M be a fixed left R-module. For a left R-module X, weintroduce the notion of M-prime (resp. M-semiprime) submodule of Xsuch that in the case M = R, it coincides with prime (resp. semiprime)submodule of X. Other concepts encountered in the general theory areM-m-system sets, M-n-system sets, M-prime radical and M-Baer’s lowernilradical of modules. Relationships between these concepts and basicproperties are established. In particular, we identify certain submodulesof M, called “primeM-ideals”, that play a role analogous to that of prime(two-sided) ideals in the ring R. Using this definition, we show that if Msatisfies condition H (defined later) and HomR(M,X) ≠ 0 for all mod-ules X in the category σ[M], then there is a one-to-one correspondencebetween isomorphism classes of indecomposable M-injective modules inσ[M] and prime M-ideals of M. Also, we investigate the prime M-ideals,M-prime submodules and M-prime radical of Artinian modules.
THE NILPOTENCY OF THE PRIME RADICAL OF A GOLDIE MODULE
John A., Beachy,Mauricio, Medina-Barcenas Korean Mathematical Society 2023 대한수학회보 Vol.60 No.1
With the notion of prime submodule defined by F. Raggi et al. we prove that the intersection of all prime submodules of a Goldie module M is a nilpotent submodule provided that M is retractable and M<sup>(Λ)</sup>-projective for every index set Λ. This extends the well known fact that in a left Goldie ring the prime radical is nilpotent.
Stromal <i>Gli2</i> activity coordinates a niche signaling program for mammary epithelial stem cells
Zhao, Chen,Cai, Shang,Shin, Kunyoo,Lim, Agnes,Kalisky, Tomer,Lu, Wan-Jin,Clarke, Michael F.,Beachy, Philip A. American Association for the Advancement of Scienc 2017 Science Vol.356 No.6335
<P>The stem cell niche is a complex local signaling microenvironment that sustains stem cell activity during organ maintenance and regeneration. The mammary gland niche must support its associated stem cells while also responding to systemic hormonal regulation that triggers pubertal changes. We find that Gli2, the major Hedgehog pathway transcriptional effector, acts within mouse mammary stromal cells to direct a hormone-responsive niche signaling program by activating expression of factors that regulate epithelial stem cells as well as receptors for the mammatrophic hormones estrogen and growth hormone. Whereas prior studies implicate stem cell defects in human disease, this work shows that niche dysfunction may also cause disease, with possible relevance for human disorders and in particular the breast growth pathogenesis associated with combined pituitary hormone deficiency.</P>
Jin, Zheung Lu,Hong, Joon Ki,Yun, Dae Jin,Lee, Sang Yeol,Choi, Young Ju,Bahk, Jeong Dong,Beachy, Roger N.,Cho, Moo Je,Lim, Chae Oh 한국식물학회 2002 Journal of Plant Biology Vol.45 No.2
Nicotiana benthamiana plants were transformed with the movement protein (MP) gene of tobacco mosaic virus (TMV), using Agrobacterium-mediated transformation. Plants regenerated from the transformed cells accumulated 30-kDa MP and complemented the activity of TMV MP when infected with chimeric TMVs containing defective MP. These transgenic plants displayed stunting, pale-green leaves, and starch accumulations, indicating that TMV MP altered the carbon partitioning for leaves involved in TMV cell-to-cell movement.
Pathogenicity in Nicotiana benthamiana Conferred by Tobacco Mosaic Virus Movement Protein Transgene
Lee, Sung-Ho,Choi, Young-Ju,Shon, Young-Goel,Hwang, Su-Jeong,Roger N. Beachy,Cho, Moo-Je,Lim, Chae-Oh Gyeongsang National University Chinju, Korea 1998 Plant molecular biology and biotechnology research Vol.1998 No.
Control of inflammation by stromal Hedgehog pathway activation restrains colitis
Lee, John J.,Rothenberg, Michael E.,Seeley, E. Scott,Zimdahl, Bryan,Kawano, Sally,Lu, Wan-Jin,Shin, Kunyoo,Sakata-Kato, Tomoyo,Chen, James K.,Diehn, Maximilian,Clarke, Michael F.,Beachy, Philip A. National Academy of Sciences 2016 PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF Vol.113 No.47
<P>Inflammation disrupts tissue architecture and function, thereby contributing to the pathogenesis of diverse diseases; the signals that promote or restrict tissue inflammation thus represent potential targets for therapeutic intervention. Here, we report that genetic or pharmacologic Hedgehog pathway inhibition intensifies colon inflammation (colitis) in mice. Conversely, genetic augmentation of Hedgehog response and systemic small-molecule Hedgehog pathway activation potently ameliorate colitis and restrain initiation and progression of colitis-induced adenocarcinoma. Within the colon, the Hedgehog protein signal does not act directly on the epithelium itself, but on underlying stromal cells to induce expression of IL-10, an immune-modulatory cytokine long known to suppress inflammatory intestinal damage. IL-10 function is required for the full protective effect of small-molecule Hedgehog pathway activation in colitis; this pharmacologic augmentation of Hedgehog pathway activity and stromal IL-10 expression are associated with increased presence of CD4(+) Foxp3(+) regulatory T cells. We thus identify stromal cells as cellular coordinators of colon inflammation and suggest their pharmacologic manipulation as a potential means to treat colitis.</P>