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Independence with respect to family of mappings in abstract algebras

100%

Głazek K.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS INTRODUCTION .................................................................................................................................................................................................. 5 I. 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.............................................................................................................................................................. 27 II. 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....................................................................................................................... 31 III. 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................................................................................................... 37 IV. 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....................................................................................... 47 REFERENCES...................................................................................................................................................................................................... 54

2

Some old and new problems in the independence theory

42%

Głazek K.

Colloquium Mathematicum

|

1979

|

tom 42

|

nr 1

127-189

3

Separable variables algebras

37%

Fajtlowicz S., Głazek K., Urbanik K.

Colloquium Mathematicum

|

1966

|

tom 15

|

nr 2

161-171

4

Independent subalgebras of a general algebra

37%

Głazek K., Iwanik A.

Colloquium Mathematicum

|

1974

|

tom 29

|

nr 2

189-194

5

On weak automorphisms of quasi-linear algebras

36%

Głazek K.

Colloquium Mathematicum

|

1971

|

tom 23

|

nr 2

191-197

6

Quasi-constants in general algebras

31%

Głazek K., Iwanik A.

Colloquium Mathematicum

|

1974

|

tom 29

|

nr 1

45-50

Ograniczanie wyników

5 Colloquium Mathematicum

6 Głazek K.

2 Iwanik A.

1 Fajtlowicz S.

1 Urbanik K.

1 1979

2 1974

2 1971

1 1966

Independence with respect to family of mappings in abstract algebras

Some old and new problems in the independence theory

Separable variables algebras

Independent subalgebras of a general algebra

On weak automorphisms of quasi-linear algebras

Quasi-constants in general algebras