AXIOMATIZABILITY OF THE CLASS OF SUBDIRECTLY IRREDUCIBLE S-ACTS OVER A COMMUTATIVE MONOID

被引：0

作者：

Stepanova, A. A. ^{[1
]}

Efremov, E. L. ^{[1
]}

机构：

[1] Far Eastern Fed Univ, Vladivostok, Russia

来源：

ALGEBRA AND LOGIC | 2023年 / 62卷 / 02期

关键词：

S-act; commutative monoid; subdirectly irreducible S-act; axiomatizable class;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An axiomatizability criterion is found for the class of subdirectly irreducible S-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable remains open even for the case of a commutative monoid.

引用

页码：179 / 200

页数：22

共 35 条

[1] Axiomatizability of the Class of Subdirectly Irreducible S-Acts over a Commutative Monoid
A. A. Stepanova
E. L. Efremov
Algebra and Logic, 2023, 62 : 179 - 200
[2] Axiomatizability of the Class of Subdirectly Irreducible S-Acts over a Commutative Monoid
Stepanova, A. A.
Efremov, E. L.
ALGEBRA AND LOGIC, 2024, 62 (2) : 179 - 200
[3] Axiomatizability of the Class of Subdirectly Irreducible Acts over an Abelian Group
A. A. Stepanova
D. O. Ptakhov
Algebra and Logic, 2020, 59 : 395 - 403
[4] Axiomatizability of the Class of Subdirectly Irreducible Acts over an Abelian Group
Stepanova, A. A.
Ptakhov, D. O.
ALGEBRA AND LOGIC, 2020, 59 (05) : 395 - 403
[5] Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group
Stepanova, A. A.
SIBERIAN MATHEMATICAL JOURNAL, 2015, 56 (03) : 516 - 525
[6] Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group
A. A. Stepanova
Siberian Mathematical Journal, 2015, 56 : 516 - 525
[7] On injective and subdirectly irreducible S-acts over left zero semigroups
Moghaddasi, Gholamreza
TURKISH JOURNAL OF MATHEMATICS, 2012, 36 (03) : 359 - 365
[8] Axiomatizability of the class of weakly injective S-acts
E. L. Efremov
A. A. Stepanova
Siberian Mathematical Journal, 2017, 58 : 611 - 618
[9] Axiomatizability of the class of weakly injective S-acts
Efremov, E. L.
Stepanova, A. A.
SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (04) : 611 - 618
[10] COVERS FOR S-ACTS AND CONDITION (A) FOR A MONOID S
Bailey, Alex
Gould, Victoria
Hartmann, Miklos
Renshaw, James
Shaheen, Lubna
GLASGOW MATHEMATICAL JOURNAL, 2015, 57 (02) : 323 - 341

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