ON WEAKLY INJECTIVE AND DIVISIBILITY OF S-ACTS

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Moghaddasi Gh.; DELAVARI S.

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Seminar Paper

Paper Information

Seminar: ANNUAL IRANIAN MATHEMATICS CONFERENCE
Year:2016 | Issue:47

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Title

ON WEAKLY INJECTIVE AND DIVISIBILITY OF S-ACTS

Author(s)

Moghaddasi Gh. | DELAVARI S. | Issue Writer Certificate

Keywords

S-ACT

WEAKLY INJECTIVE S-ACT

DIVISIBLITY

Abstract

IN THIS PAPER WE INVESTIGATE ACTIONS OF A MONOID OF THE FORM S=GÈI, WHERE G IS A GROUP AND I IS AN IDEAL OF S. SO, NATURALLY, EVERY S-ACT CAN BE CONSIDERED AS AN I1-ACT. THE CENTRAL QUESTION HERE IS THAT WHAT IS THE RELATION BETWEEN WEAKLY INJECTIVE AND DIVISIBLE I1-ACTS AND WEAKLY INJECTIVE AND DIVISIBLE S-ACTS?WE ARE GOING TO RESPOND THIS QUESTION AND SHOW THAT, GIVEN AN S-ACT A, (PRINCIPALLY, FINITELY GENERATED) WEAKLY INJECTIVE AND DIVISIBLE PROPERTY OF A IS EXTENDABLE FROM I1-ACTS TO S-ACTS IN GENERAL. WE ALSO SHOW THAT IF I IS STRONGLY REGULAR THEN AN S-ACT A WITH A UNIQUE FIXED ELEMENT Q IS WEAKLY INJECTIVE IF AND ONLY IF A IS INJECTIVE RELATIVE TO INCLUSION I → S. ALSO IF I1 IS A LEFT CANCELLABLE PRINCIPAL IDEAL MONOID. THEN, DIVISIBLITY OF A AS AN I1-ACT IMPLIES WEAKLY INJECTIVITY OF A AS AN S-ACT.

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APA: Copy

Moghaddasi, Gh., & DELAVARI, S.. (2016). ON WEAKLY INJECTIVE AND DIVISIBILITY OF S-ACTS. ANNUAL IRANIAN MATHEMATICS CONFERENCE. SID. https://sid.ir/paper/946786/en

Vancouver: Copy

Moghaddasi Gh., DELAVARI S.. ON WEAKLY INJECTIVE AND DIVISIBILITY OF S-ACTS. 2016. Available from: https://sid.ir/paper/946786/en

IEEE: Copy

Gh. Moghaddasi, and S. DELAVARI, “ON WEAKLY INJECTIVE AND DIVISIBILITY OF S-ACTS,” presented at the ANNUAL IRANIAN MATHEMATICS CONFERENCE. 2016, [Online]. Available: https://sid.ir/paper/946786/en

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