Transfer properties in radical theory
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2004), pp. 46-56.

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

A functor is said to reflect radical classes if under this functor the inverse image of a radical class is always a radical class.Prototypical examples of such functors include polynomial and matrix functors and various forgetful functors.This paper is for the most part a survey of known results concerning radical reflections,but there are a few new results,including a generalization to right alternative rings of a well known result of Andrunakievici on upper radicals of simple associative rings.
@article{BASM_2004_1_a5,
     author = {R. J. Gardner},
     title = {Transfer properties in radical theory},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {46--56},
     publisher = {mathdoc},
     number = {1},
     year = {2004},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2004_1_a5/}
}
TY  - JOUR
AU  - R. J. Gardner
TI  - Transfer properties in radical theory
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2004
SP  - 46
EP  - 56
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2004_1_a5/
LA  - en
ID  - BASM_2004_1_a5
ER  - 
%0 Journal Article
%A R. J. Gardner
%T Transfer properties in radical theory
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2004
%P 46-56
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2004_1_a5/
%G en
%F BASM_2004_1_a5
R. J. Gardner. Transfer properties in radical theory. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2004), pp. 46-56. https://geodesic-test.mathdoc.fr/item/BASM_2004_1_a5/

[1] Janelidze G., Márki L., Tholen W., “Semi-abelian categories”, J. Pure Appl. Algebra, 168 (2002), 367–386 | DOI | MR | Zbl

[2] Gardner B. J., Radical Theory, Longman, 1989 | MR

[3] Gardner B. J., Wiegandt R., Radical theory of Rings, Dekker, 2003 | MR

[4] Gardner B. J., Stewart P. N., “Reflected radical classes”, Acta. Math. Acad. Sci. Hungar., 28 (1976), 293–298 | DOI | MR | Zbl

[5] Puczyłowski E. R., “Nil ideals of power series rings”, J. Austral. Math. Soc., 34 (1983), 287–292 | DOI | MR | Zbl

[6] Arnautov V. I., “Algebraic radicals in topological rings”, Mat. issled., 4:2 (1969), 116–122 (In Russian) | MR | Zbl

[7] Krempa J., “Radicals of semi-group rings”, Fund. Math., 85 (1974), 57–71 | MR | Zbl

[8] Gardner B. J., “Radicals of abelian groups and associative rings”, Acta Math. Acad. Sci. Hungar., 24 (1973), 259–268 | DOI | MR

[9] Divinsky N., Suliński A., “Kurosh radicals of rings with operators”, Canad. J. Math., 17 (1965), 278–280 | MR | Zbl

[10] Thedy A., “Radicals of right alternative and Jordan rings”, Comm. in Algebra, 12 (1984), 857–887 | DOI | MR | Zbl

[11] Skosyrskii V. G., “Nilpotence in Jordan and right alternative algebras”, Algebra i Logika, 18 (1979), 49–57 (In Russian) | DOI | MR

[12] Thedy A., “Jordan radicals of $U$-algebras”, Comm. in Algebra, 18 (1990), 711–739 | DOI | MR | Zbl

[13] Gardner B. J., “A note on radicals and polynomial rings”, Math. Scand., 31 (1972), 83–88 | MR | Zbl

[14] McCrimmon K., “Amitsur shrinkage of Jordan radicals”, Comm. in Algebra, 12 (1984), 777–826 | DOI | MR | Zbl

[15] Csákány B., “Varieties of affine modules”, Acta. Sci. Math. (Szeged), 37 (1975), 3–10 | MR | Zbl

[16] Csákány B., Megyesi L., “Varieties of idempotent medial quasigroups”, Acta. Sci. Math. (Szeged), 37 (1975), 17–23 | MR | Zbl

[17] Ježek J., Kepka T., “Varieties of abelian quasigroups”, Czechoslovak. Math. J., 27 (1977), 473–503 | MR | Zbl

[18] Gardner B. J., “Radical decompositions of idempotent algebras”, J. Austral. Math. Soc., Series A, 36 (1984), 213–236 | DOI | MR | Zbl

[19] Belluce L. P., Di Nola A., Georgescu G., “Perfect $MV$-algebras and $l$-rings”, J. Applied Non-Classical Logics, 9 (1999), 159–172 | MR | Zbl

[20] Mundici D., “Interpretation of $AF$ $C^*$-algebras in Łukasiewicz sentential calculus”, J. Functional Analysis, 65 (1986), 15–63 | DOI | MR | Zbl

[21] Di Nola A., Lettieri A., “Perfect $MV$-algebras are categorically equivalent to abelian $l$-groups”, Studia Logica, 53 (1994), 417–432 | DOI | MR | Zbl

[22] Widarma G., “Nondegenerate radicals of right alternative rings”, Acta Math. Hungar., 100 (2003), 19–30 | DOI | MR | Zbl

[23] Gardner B. J., “Semi-simple radical classes of algebras and attainability of identities”, Pacific J. Math., 61 (1975), 401–416 | MR

[24] Gardner B. J., “Some degeneracy and pathology in non-associative radical theory”, Annales. Univ. Sci. Budapest. Sect. Math., 22–23 (1979–1980), 65–74 | MR

[25] Skosyrskii V. G., “Right alternative algebras”, Algebra i Logika, 23 (1983), 478–489 (In Russian) | MR

[26] Andrunakievich V. A., “Radicals of associative rings. II: Examples of special radicals”, Amer. Math. Soc. Translations Series, 2:52 (1966), 129–149

[27] Suliński A., “The Brown-McCoy radical in categories”, Fund. Math., 49 (1966), 23–41 | MR

[28] Leavitt W. G., “A minimally embeddable ring”, Period. Math. Hungar., 12 (1981), 129–140 | DOI | MR | Zbl

[29] Armendariz E. P., “Closure properties in radical theory”, Pacific J. Math., 26 (1968), 1–7 | MR | Zbl

[30] Henriksen M., “Conditions that guarantee that all nilpotents commute with every element of an alternative ring”, Algebra Univ., 7 (1977), 119–132 | DOI | MR | Zbl