# Pseudocomplements in sum-ordered partial semirings

Discussiones Mathematicae - General Algebra and Applications (2007)

- Volume: 27, Issue: 2, page 169-186
- ISSN: 1509-9415

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topJānis Cīrulis. "Pseudocomplements in sum-ordered partial semirings." Discussiones Mathematicae - General Algebra and Applications 27.2 (2007): 169-186. <http://eudml.org/doc/276896>.

@article{JānisCīrulis2007,

abstract = {We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.},

author = {Jānis Cīrulis},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {Glivenko theorem; partial monoid; partial semiring; pseudocomplementation; semigroup; Stone semiring; sum-ordering},

language = {eng},

number = {2},

pages = {169-186},

title = {Pseudocomplements in sum-ordered partial semirings},

url = {http://eudml.org/doc/276896},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Jānis Cīrulis

TI - Pseudocomplements in sum-ordered partial semirings

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2007

VL - 27

IS - 2

SP - 169

EP - 186

AB - We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.

LA - eng

KW - Glivenko theorem; partial monoid; partial semiring; pseudocomplementation; semigroup; Stone semiring; sum-ordering

UR - http://eudml.org/doc/276896

ER -

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