One-sided principal ideals in the direct product of two semigroups

Imrich Fabrici

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 4, page 337-342
  • ISSN: 0862-7959

Abstract

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A necessary and sufficient condition is given for a) a principal left ideal L ( s , t ) in S × T to be equal to the direct product of the corresponding principal left ideals L ( s ) × L ( t ) , b) an ℒ -class L ( s , t ) to be equal to the direct product of the corresponding ℒ -classes L s × L t .

How to cite

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Fabrici, Imrich. "One-sided principal ideals in the direct product of two semigroups." Mathematica Bohemica 118.4 (1993): 337-342. <http://eudml.org/doc/29310>.

@article{Fabrici1993,
abstract = {A necessary and sufficient condition is given for a) a principal left ideal $L(s,t)$ in $S\times T$ to be equal to the direct product of the corresponding principal left ideals $L(s)\times L(t)$, b) an $\mathcal \{L\}$-class $L_\{(s,t)\}$ to be equal to the direct product of the corresponding $\mathcal \{L\}$-classes $L_s\times L_t$.},
author = {Fabrici, Imrich},
journal = {Mathematica Bohemica},
keywords = {principal left ideal; direct product; direct product of two semigroups; -classes; principal left ideal; direct product},
language = {eng},
number = {4},
pages = {337-342},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {One-sided principal ideals in the direct product of two semigroups},
url = {http://eudml.org/doc/29310},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Fabrici, Imrich
TI - One-sided principal ideals in the direct product of two semigroups
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 4
SP - 337
EP - 342
AB - A necessary and sufficient condition is given for a) a principal left ideal $L(s,t)$ in $S\times T$ to be equal to the direct product of the corresponding principal left ideals $L(s)\times L(t)$, b) an $\mathcal {L}$-class $L_{(s,t)}$ to be equal to the direct product of the corresponding $\mathcal {L}$-classes $L_s\times L_t$.
LA - eng
KW - principal left ideal; direct product; direct product of two semigroups; -classes; principal left ideal; direct product
UR - http://eudml.org/doc/29310
ER -

References

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  1. Abrhám I., On (H, T)-ideals in the direct product of semigroups, Mat. časopis 21 (1971), 199-211. (1971) 
  2. Clifford A.H., Preston G.B., The algebraic theory of semigroups, American Math. Soc., Providence, R.I., 1961. (1961) Zbl0111.03403MR0132791
  3. Fabrici I., On semiprime ideals in the direct product of semigroups, Mat. časopis 18 (1968), 201-203. (1968) MR0237674
  4. Ivan J., On the direct product of semigroups, Mat.-fyz. časopis (1953), 57-66. (1953) MR0062733
  5. Petrich M., Prime ideals in the cartesian product of two semigroups, Czechoslov. Math. J. 12 (1962), 150-152. (1962) MR0140597
  6. Petrich M., Introduction to semigroups, Charles E. Merrill Publishing CO. A Bell and Howell Company, Ohio. Zbl0321.20037MR0393206
  7. Plemmons R., Maximal ideals in the direct product of two semigroups, Czechoslov. Math. J. 17 (1967), 257-260. (1967) Zbl0189.02001MR0214681

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