Independence with respect to family of mappings in abstract algebras

Kazimierz Głazek

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1971

Abstract

top
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

How to cite

top

Kazimierz Głazek. Independence with respect to family of mappings in abstract algebras. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1971. <http://eudml.org/doc/268460>.

@book{KazimierzGłazek1971,
abstract = {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},
author = {Kazimierz Głazek},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Independence with respect to family of mappings in abstract algebras},
url = {http://eudml.org/doc/268460},
year = {1971},
}

TY - BOOK
AU - Kazimierz Głazek
TI - Independence with respect to family of mappings in abstract algebras
PY - 1971
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
UR - http://eudml.org/doc/268460
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.