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Keywords:
amalgamated ring; unipotent; symmetric ring; reversible ring
amalgamated ring; unipotent; symmetric ring; reversible ring
Summary:
Let $f \colon A\rightarrow B$ and $g\colon A\rightarrow C$ be two ring homomorphisms and let $K$ and $K'$ be two ideals of $B$ and $C$, respectively, such that $f^{-1}(K) = g^{-1}(K')$. We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring $A\bowtie ^{f,g}(K, K')$ of $A$ with $(B, C)$ along $(K, K')$ with respect to $(f, g)$.
References:
[1] Călugăreanu, G.: UU rings. Carpathian J. Math. 31 (2015), 157-163. MR 3408811 | Zbl 1349.16059
[2] Chun, Y., Jeon, Y. C., Kang, S., Lee, K. N., Lee, Y.: A concept unifying the Armendariz and $NI$ conditions. Bull. Korean Math. Soc. 48 (2011), 115-127. DOI 10.4134/BKMS.2011.48.1.115 | MR 2778501 | Zbl 1214.16021
[3] Cohn, P. M.: Reversible rings. Bull. Lond. Math. Soc. 31 (1999), 641-648. DOI 10.1112/S0024609399006116 | MR 1711020 | Zbl 1021.16019
[4] D'Anna, M., Finocchiaro, C. A., Fontana, M.: Amalgamated algebras along an ideal. Commutative Algebra and its Applications Walter De Gruyter, Berlin (2009), 155-172. DOI 10.1515/9783110213188.155 | MR 2606283 | Zbl 1177.13043
[5] Farshad, N., Safarisabet, S. A., Moussavi, A.: Amalgamated rings with clean-type properties. Hacet. J. Math. Stat. 50 (2021), 1358-1370. DOI 10.15672/hujms.676342 | MR 4331405 | Zbl 1499.16067
[6] Goodearl, K. R.: Von Neumann Regular Rings. Monographs and Studies in Mathematics 4. Pitman, London (1979). MR 0533669 | Zbl 0411.16007
[7] Kabbaj, S., Louartiti, K., Tamekkante, M.: Bi-amalgamated algebras along ideals. J. Commut. Algebra 9 (2017), 65-87. DOI 10.1216/JCA-2017-9-1-65 | MR 3631827 | Zbl 1390.13008
[8] Kafkas, G., Ungor, B., Halicioglu, S., Harmanci, A.: Generalized symmetric rings. Algebra Discrete Math. 12 (2011), 72-84. MR 2952903 | Zbl 1259.16042
[9] Kose, H., Ungor, B., Kurtulmaz, Y., Harmanci, A.: A perspective on amalgamated rings via symmetricity. Rings, Modules and Codes Contemporary Mathematics 727. AMS, Providence (2019), 237-247. DOI 10.1090/conm/727 | MR 3938153 | Zbl 1429.16031
[10] Lambek, J.: On the representation of modules by sheaves of factor modules. Can. Math. Bull. 14 (1971), 359-368. DOI 10.4153/CMB-1971-065-1 | MR 0313324 | Zbl 0217.34005
[11] Marks, G.: Reversible and symmetric rings. J. Pure Appl. Algebra 174 (2002), 311-318. DOI 10.1016/S0022-4049(02)00070-1 | MR 1929410 | Zbl 1046.16015
[12] Ouyang, L., Chen, H.: On weak symmetric rings. Commun. Algebra 38 (2010), 697-713. DOI 10.1080/00927870902828702 | MR 2598907 | Zbl 1197.16033
[13] Zhao, L., Yang, G.: On weakly reversible rings. Acta Math. Univ. Comen., New Ser. 76 (2007), 189-192. MR 2385031 | Zbl 1156.16026
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