Peirce Decompositions for Evolution Algebras

REFERENCES

[1] Boudi, N.—Cabrera Casado, Y.—Siles Molina, M.: Natural families in evolution algebras, Publ. Math. 66 (2022), 159–181.10.5565/PUBLMAT6612206Suche in Google Scholar

[2] Bustamante, M. D.—Mellon, P.—Velasco, M. V.: Determining when an algebra is an evolution algebra; https://arxiv.org/pdf/2102.04493.Suche in Google Scholar

[3] Cabrera Casado, Y.—Cadavid, P.—Reis, T.: Derivations and loops of some evolution algebras, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 117 (2023), Art. No. 119.10.1007/s13398-023-01446-2Suche in Google Scholar

[4] Cabrera Casado, Y.—Cardoso Gonçalves, M. I.—Gonçalves, D.—Martín Barquero, D.—Martín González, C.: Chains in Evolution algebras, Linear Algebra Appl. 622 (2021), 104–149.10.1016/j.laa.2021.03.026Suche in Google Scholar

[5] Cabrera Casado, Y.—Kanuni, M.—Siles Molina, M.: Basic ideals in evolution algebras, Linear Algebra Appl. 570 (2019), 148–180.10.1016/j.laa.2019.01.010Suche in Google Scholar

[6] Cabrera Casado, Y.—Siles Molina, M.—Velasco, M. V.: Evolution algebras of arbitrary dimension and their decompositions, Linear Algebra Appl. 495 (2016) 122–162.10.1016/j.laa.2016.01.007Suche in Google Scholar

[7] Cadavid, P.—Rodiño Montoya, M. L.—Rodríguez, P. M.: The connection between evolution algebras, random walks and graphs, J. Algebra Appl. 19(2) (2020), Art. ID 2050023.10.1142/S0219498820500231Suche in Google Scholar

[8] Casas, J. M.—Ladra, M.—Omirov, B. A.—Rozikov, U. A.: On evolution algebras, Algebra Colloq. 21(2) (2014), 331–342.10.1142/S1005386714000285Suche in Google Scholar

[9] Casas, J. M.—Ladra, M.—Rozikov, U. A.: A chain of evolution algebras, Linear Algebra Appl. 435 (2011), 852–870.10.1016/j.laa.2011.02.012Suche in Google Scholar

[10] Ceballos, M.—Falcón, R. M.—Núũez-Valdés, J.—Tenorio, A. F.: A historical perspective of Tian’s evolution algebras, Expo. Math. 40(3) (2022), 819–843.10.1016/j.exmath.2021.11.004Suche in Google Scholar

[11] Da Motta Ferreira, J. C.—Micali, A.: Sur les algèbres nucléaires, Indag. Math. 7(3) (1996), 331–342.10.1016/0019-3577(96)83724-4Suche in Google Scholar

[12] Elduque, A.—Labra, A.: Evolution algebras and graphs, J. Algebra Appl. 14(7) (2015), Art. ID 1550103.10.1142/S0219498815501030Suche in Google Scholar

[13] Etherington, I. H. M.: Genetic algebras, Proc. Roy. Soc. Edinburgh Sect. A 59 (1939), 242–258.10.1017/S0370164600012323Suche in Google Scholar

[14] Jacobson, N.: Structure of Rings. Amer. Math. Soc. Colloq. Publ., Vol. 37, Amer. Math. Soc. Providence, R. I., 1956.Suche in Google Scholar

[15] Kurdoyberdiyev, A. KH.—Omirov, B. A.—Qaralleh, I.: Few remarks on evolution algebras, J. Algebra Appl. 14(4) (2015), Art. ID 1550053.10.1142/S021949881550053XSuche in Google Scholar

[16] Lyubich, Y. I.: Mathematical Structures in Population Genetics. Biomathematics, Vol. 22, Springer-Verlag, Berlin, 1992.10.1007/978-3-642-76211-6Suche in Google Scholar

[17] Mellon, P.—Velasco, M. V.: Analytic aspects of evolution algebras, Banach J. Math. Anal. 13(1) (2019), 113–132.10.1215/17358787-2018-0018Suche in Google Scholar

[18] Mukhamedov, F.—Qaralleh, I.: On S-evolution algebras and their envelopping algebras, Mathematics 9 (2021), Art. No. 1195.10.3390/math9111195Suche in Google Scholar

[19] Murodov, SH. N.: Classification of two-dimensional real evolution algebras and dynamics of some two dimensional chains of evolution algebras, Uzbek. Math. J. 25(2) (2014), 102–111.10.1142/S0129167X14500128Suche in Google Scholar

[20] Ouattara, M.—Savadogo, S.: Power-associative evolution algebras. In: Associative and Non-Associative Algebras and Applications, MAMAA 2018, Springer Proc. Math. Stat., Vol. 311, Springer, 2020, pp. 23–49.10.1007/978-3-030-35256-1_2Suche in Google Scholar

[21] Ouattara, M.—Savadogo, S.: Evolution train algebras, Gulf J. Math. 8(1) (2020), 37–51.10.56947/gjom.v8i1.299Suche in Google Scholar

[22] Paniello, I.: Markov evolution algebras, Linear Multilinear Algebra 70(19) (2022), 4633–4653.10.1080/03081087.2021.1893636Suche in Google Scholar

[23] Reed, M. L.: Algebraic structure of genetic inheritance, Bull. Amer. Math. Soc. 34(2) (1997), 107–130.10.1090/S0273-0979-97-00712-XSuche in Google Scholar

[24] Rich, M.: Rings with idempotents in their nuclei, Trans. Amer. Math. Soc. 208 (1975) 81–90.10.1090/S0002-9947-1975-0371972-9Suche in Google Scholar

[25] Schafer, R. D.: An Introduction to Nonassociative Algebras. Pure and Appl. Math., Vol. 22, Academic Press, New York-London, 1966.Suche in Google Scholar

[26] Tian, J. P.—Vojtěchovský, P.: Mathematical concepts of evolution algebras in non-Mendelian genetics, Quasigroups Related systems 14 (2006), 111–122.Suche in Google Scholar

[27] Tian, J. P.: Evolution Algebras and their Applications, Lecture Notes in Math., Vol. 1921, Springer, Berlin, 2008.10.1007/978-3-540-74284-5Suche in Google Scholar

[28] Wörz-Busekros, A.: Algebras in Genetics. Lecture Notes in Biomathematics, Vol. 36, Springer-Verlag, New York, 1980.10.1007/978-3-642-51038-0Suche in Google Scholar