On hereditarily pure associative algebras over Dedekind rings
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 475-490.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the description hereditary pure associative algebras over Dedekind rings is investigated. In particular, nilalgebras, idempotent algebras and commutative algebras with such property are characterized.
Keywords: associative algebra, Dedekind ring, hereditary pure associative algebra.
@article{SEMR_2013_10_a13,
     author = {L. M. Martynov},
     title = {On hereditarily pure associative algebras over {Dedekind} rings},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {475--490},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a13/}
}
TY  - JOUR
AU  - L. M. Martynov
TI  - On hereditarily pure associative algebras over Dedekind rings
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2013
SP  - 475
EP  - 490
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2013_10_a13/
LA  - ru
ID  - SEMR_2013_10_a13
ER  - 
%0 Journal Article
%A L. M. Martynov
%T On hereditarily pure associative algebras over Dedekind rings
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2013
%P 475-490
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2013_10_a13/
%G ru
%F SEMR_2013_10_a13
L. M. Martynov. On hereditarily pure associative algebras over Dedekind rings. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 475-490. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a13/

[1] L. M. Martynov, “O ponyatiyakh primarnosti, polnoty, redutsirovannosti i chistoty dlya proizvolnykh algebr”, Universalnaya algebra i eë prilozheniya, Trudy mezhdunarodnogo seminara (Volgograd, 6–11 sentyabrya 1999), Peremena, Volgograd, 2000, 179–190

[2] A. I. Maltsev, “Ob umnozhenii klassov algebraicheskikh sistem”, Sib. mat. zh., 8:2 (1967), 346–365

[3] L. N. Shevrin, L. M. Martynov, “O dostizhimykh klassakh algebr”, Sib. mat. zhurn., 12:6 (1971), 1363–1381 | MR | Zbl

[4] L. N. Shevrin, L. M. Martynov, “Attainability and solvability for classes of algebras”, Semigroups: Structure and universal algebraic problems (Szeged, Hungary, 1981), Colloq. Math. Soc. J. Bolyai, 39, North-Holland, Amsterdam e. a., 1985, 397–459 | MR

[5] L. M. Martynov, “O probleme spektrov razreshimosti dlya mnogoobrazii algebr”, Algebra i logika, 29:2 (1990), 162–178 | MR | Zbl

[6] L. M. Martynov, “Ob odnom radikale algebr so svoistvom transverbalnosti po minimalnym mnogoobraziyam”, Vest. Omsk. un-ta, 2004, no. 3, 19–21

[7] A. G. Kurosh, “Radikaly v teorii grupp”, Sib. mat. zhurn., 3:6 (1962), 912–931 | MR | Zbl

[8] A. I. Kornev, “O modulyakh s chistymi podmodulyami”, Universalnaya algebra i eë prilozheniya, Trudy mezhdunarodnogo seminara (Volgograd, 6–11 sentyabrya 1999), Peremena, Volgograd, 2000, 144–152

[9] A. I. Kornev, “Prostye po chistote moduli redutsirovannykh mnogoobrazii modulei nad kommutativnymi koltsami”, Vest. Omsk. un-ta, 2000, no. 4, 13–15 | MR | Zbl

[10] A. A. Tuganbaev, “Primitively pure submodules and primitively divisible modules”, Journal of Mathematical Sciences, 110:3 (2002), 2746–2754 | DOI | MR | Zbl

[11] O. V. Knyazev, “O chistykh algebrakh s vydelennym elementom”, Matematika i informatika: nauka i obrazovanie, 1, Izd-vo OmGPU, Omsk, 2001, 10–13

[12] O. V. Knyazev, “O chistykh algebrakh”, Vest. Omsk. un-ta, 2001, no. 3, 18–20 | Zbl

[13] O. V. Knyazev, “Ob absolyutno chistykh algebrakh s vydelennym elementom”, Matematika i informatika: nauka i obrazovanie, 2, Izd-vo OmGPU, Omsk, 2002, 23–25

[14] O. V. Knyazev, “Nasledstvenno chistye kommutativnye monoidy”, Matematika i informatika: nauka i obrazovanie, 3, Izd-vo OmGPU, Omsk, 2003, 16–19

[15] O. V. Knyazev, “Nasledstvenno chistye monoidy”, Sib. elektron. matem. izv., 2 (2005), 83–87 | MR | Zbl

[16] O. V. Knyazev, “Polugruppy s nasledstvenno chistymi podpolugruppami”, Izv. Ural. gos. un-ta (Matematika i mekhanika), 2005, no. 8 (38), 69–79 | MR | Zbl

[17] O. V. Knyazev, “Prostye po chistote vpolne regulyarnye polugruppy”, Vest. Omsk. un-ta, 2006, no. 4, 17–20

[18] O. V. Knyazev, “O chistykh tsiklicheskikh podgruppakh grupp”, Matematika i informatika: nauka i obrazovanie, 5, Izd-vo OmGPU, Omsk, 2006, 24–26

[19] I. V. Znaeva, “Nasledstvenno chistye algebry Li”, Matematika i informatika: nauka i obrazovanie, 6, Izd-vo OmGPU, Omsk, 2007, 12–15

[20] L. M. Martynov, “Nasledstvenno chistye assotsiativnye koltsa”, Matematika i informatika: nauka i obrazovanie, 9, Izd-vo OmGPU, Omsk, 2010, 25–35

[21] L. M. Martynov, “Nasledstvenno chistye assotsiativnye algebry nad dedekindovym koltsom, maksimalnye idealy kotorogo imeyut konechnye indeksy”, Algebra i logika, 50:6 (2011), 781–801 | MR

[22] O. Zarisskii, P. Samyuel, Kommutativnaya algebra, v. 1, IL, M., 1963 | Zbl

[23] N. Dzhekobson, Teoriya kolets, IIL, M., 1961

[24] T. R. Sundararaman, “Precomplete varieties of $R$-algebras”, Alg. Univers., 27:2 (1974), 243–256 | MR

[25] V. A. Artamonov, “Reshetki mnogoobrazii lineinykh algebr”, Uspekhi mat. nauk., 33:2 (1978), 135–167 | MR | Zbl

[26] L. M. Martynov, “O primarnykh i redutsirovannykh mnogoobraziyakh monoassotsiativnykh algebr”, Sib. mat. zh., 42:1 (2001), 103–112 | MR | Zbl

[27] L. M. Martynov, “Nasledstvenno chistye assotsiativnye kommutativnye algebry nad dedekindovymi koltsami”, Maltsevskie chteniya, Mezhdunarodnaya konferentsiya, posvyaschennaya 60-letiyu so dnya rozhdeniya S. S. Goncharova, Tezisy dokladov (11–14 oktyabrya 2011 g.), Novosibirsk, 2011, 116