# Directoids with an antitone involution

Commentationes Mathematicae Universitatis Carolinae (2007)

- Volume: 48, Issue: 4, page 555-569
- ISSN: 0010-2628

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topChajda, Ivan, and Kolařík, Miroslav. "Directoids with an antitone involution." Commentationes Mathematicae Universitatis Carolinae 48.4 (2007): 555-569. <http://eudml.org/doc/250201>.

@article{Chajda2007,

abstract = {We investigate $\sqcap $-directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation $\sqcup $ can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids with an antitone involution.},

author = {Chajda, Ivan, Kolařík, Miroslav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {directoid; antitone involution; D-quasiring; symmetrical difference; direct decomposition; directoid; antitone involution; D-quasiring; symmetrical difference; direct decomposition},

language = {eng},

number = {4},

pages = {555-569},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Directoids with an antitone involution},

url = {http://eudml.org/doc/250201},

volume = {48},

year = {2007},

}

TY - JOUR

AU - Chajda, Ivan

AU - Kolařík, Miroslav

TI - Directoids with an antitone involution

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2007

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 48

IS - 4

SP - 555

EP - 569

AB - We investigate $\sqcap $-directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation $\sqcup $ can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids with an antitone involution.

LA - eng

KW - directoid; antitone involution; D-quasiring; symmetrical difference; direct decomposition; directoid; antitone involution; D-quasiring; symmetrical difference; direct decomposition

UR - http://eudml.org/doc/250201

ER -

## References

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