Independence with respect to family of mappings in abstract algebras

Kazimierz Głazek

GDML_Books, (1971), p.

Résumé

CONTENTSINTRODUCTION .................................................................................................................................................................................................. 5I. INDEPENDENCE WITH RESPECT TO A GIVEN FAMILY OF MAPPINGS (GENERAL PROPERTIES) ............................................ 7§ 1. Notation and main definitions.................................................................................................................................................................... 7§ 2. Notions of independence defined by families of mappings (Q-independence).............................................................................. 9§ 3. Maximal families of mappings for a given independence.................................................................................................................... 13§ 4. Q-independent sets of generators (Q-bases)......................................................................................................................................... 17§ 5. Exchange of Q-independent sets.............................................................................................................................................................. 27II. VARIOUS NOTIONS OF INDEPENDENCE IN ALGEBRAS AND LINEAR SPACES............................................................................. 29§ 6. Construction of some family of mappings .............................................................................................................................................. 29§ 7. Corollaries concerning v**-algebras and linear spaces....................................................................................................................... 31III. THE INDEPENDENCE NOTIONS IN ABELIAN GROUPS AND QUASI-LINEAR ALGEBRAS............................................................ 33§ 8. $S_0$- and S-independence in abelian groups.................................................................................................................................... 33§ 9. The S-, $S_0-$, G-, and R-independence in quasi-linear algebras................................................................................................... 37IV. VARIOUS NOTIONS OF INDEPENDENCE IN BOOLEAN ALGEBRAS AND SOME OF THEIR REDUCTS.................................... 46§ 10. Additional notations, and some known results.................................................................................................................................... 45§ 11. Various notions of independence in regular reducts of Boolean algebra....................................................................................... 47REFERENCES...................................................................................................................................................................................................... 54

Détail

Zbl 0213.29601

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