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Unique Representation Domains, II
Given a star operation * of finite type, we call a domain R a *-unique representation domain (*-URD) if each *-invertible ideal of R can be uniquely expressed as a *-product of pairwise *-comaximal ideals with prime radical. When * is the t-operation let us call such a domain simply a URD. Any unique factorization domain is a URD.
Generalizing and unifying results due to M. Zafrullah (1978) and J. Brewer-W. Heinzer (2002), we give conditions for a *-ideal to be a unique *-product of pairwise *-comaximal ideals with prime radical and characterize *-URDs. We show that
the class of URDs includes rings of Krull type, the generalized Krull domains introduced by El Baghdadi and weakly Matlis domains whose t-spectrum is treed.
We also study when the property of being a URD extends to some classes of overrings, such as polynomial extensions, rings of fractions and rings obtained by the construction
Studying monoids is not enough to study multiplicative properties of rings: an elementary approach.
A “υ-Operation Free” Approach to Prüfer υ-Multiplication Domains
The so-called Prüfer υ-multiplication domains (PυMDs) are usually defined as domains whose finitely generated nonzero ideals are t-invertible. These domains generalize Prüfer domains and Krull domains. The PυMDs are relatively obscure compared to their very well-known special cases. One of the reasons could be that the study of PυMDs uses the jargon of star operations, such as the υ-operation and the t-operation. In this paper, we provide characterizations of and basic results on PυMDs and related notions without star operations
Upaya Indonesia Untuk Mencapai Sumber Daya Manusia Yang Berdaya Saing Global
Paper ini merupakan review dari peneliti sebelumnya yaitu Ahmad Zafrullah Tayibnapis, Lucia Endang Wuryaningsih, dan Radita Gora yang menjelaskan tentang upaya Indonesia untuk mencapai sumber daya manusia yang berdaya saing global dalam mencapai revolusi industri 4.0 yang unggul agar dapat bersaing secara global
TUGAS REVIEW Perekonomian Indonesia , Ahmad Zafrullah
Tugas mereview salah satu artikel yang terdapat di scholar.google.com by [email protected]
Some remarks on Prüfer *-multiplication domains and class groups
Let be an integral domain with quotient field and let be an
indeterminate over . Also, let be a
defining family of quotient rings of and suppose that is a
finite type star operation on induced by . We show that is a PMD (resp., PMD) if and only if (\co_D(fg))^{\ast }=(\co_D(f)\co_D(g))^{\ast }
(resp., (\co_D(fg))^{w }=(\co_D(f)\co_D(g))^{w }) for all . A more general version of this result is given in the semistar operation setting. We give a method for recognizing PMD's which are not PMD's for a certain finite type star operation . We study domains for which the --class group \Cl^{\ast }(D) equals the --class group \Cl^{t}(D) for any finite type star operation , and we indicate examples of PMD's such that \Cl^{\ast(D)\subsetneq
\Cl^{t}(D). We also compute \Cl^v(D) for certain valuation domains
Industrial training report: Petronas Sdn Bhd / Nur Fatini Adilah Zafrullah
This report highlights the experience and skills I gained during my six months of Internship Practical at Petronas Company, from March 1st to August 9th, 2024, under the supervision of the director, Puan Hafizah Ahmad Afif.
The purpose of the project is to fulfil the core requirements for the award of a Bachelor in Business Administration (HONS) Marketing Degree by providing students with a practical aspect of the theoretical work that they have studied at the university, as well as to allow students to gain experience working in a workplace.
During my period of this internship, I learned a lot of new things. This company provides multitasking to their intern. As a result, I learned not only about finance, but I also learn about various things such as documentation, human resources, marketing, and others.
This report discusses the SWOT analysis of Petronas Company as well as skills acquired and experience gained during the training period, thereby justifying the scheme's relevance in providing students with the professional abilities required to thrive in the real world
Going Beyond Counting First Authors in Author Co-citation Analysis
The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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