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Register a new userCategory of Ideals in a Ring R
فئة المثاليات في حلقة R
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Damascus University ورقة بحثية
Publication date
2011
fields
Mathematics
and research's language is
العربية
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Shamra Editor
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في هذه الورقة العلمية تعاملنا مع ثلاثة أنواع من التشاكلات بين مثاليين في حلقة (واحدية) R و هي: تشاكل حلقي، و R ـ تشاكل مودولي، و تشاكل مثالي. و ذكرنا عدداً من الأمثلة على ذلك، و أثبتنا أن أسرة المثاليات في الحلقة R مع (التشاكلات الحلقية، R ـ تشاكلات المودلية، التشاكلات المثالية) تُشكل فئـة دعوناها فئة مثاليات من النوع (الأول، الثاني، الثالث) على الترتيب.
In this scientific paper we dealt with three different types of homomorphisms between two given ideals in a ring with unity shown as follows: ring homomorphism, R- module homomorphism and ideal homomorphism, which were supported by several examples. Furthermore, we prove that the family of ideals in a ring R with ring, R - module and ideal homomorphisms forms the category of ideals of the first, second and third type, respectively. The next step was dedicated to support all previous ideals by examples and functor between such categories.
References used
Mac Lane, S. (1998). Categories for the Working Mathematician. Springer, Verlag, New York, Second Edition
Grillet, P. A. (2007). Abstract Algebra. Springer science and Business Media, Second Edition, 105-148
Mac Lane, S and Birkhoff, G. (1999). Algebra. American Mathematical Society. Third Edition 85-124
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In this paper, we studied the concept of semi-potency of
endomorphism ring of modules. In addition to that, it has been
studied the endomorphism ring of semi injective ( projective)
modules and direct injective ( projective) modules.
أساس جاكبسون
الحلقات شبه الجامدة
Jacobson radical
Endomorphism rings
حلقة الإندومورفيزمات لمودول
المودولات نصف الإسقاطية ( الأفقية )
المودولات الأفقية ( الإسقاطية ) المباشرة
المودولات المنتظمة
Semi-potent rings
Semi injective ( projective) Modules
Regular modules
( Direct projective injective ( projective
المزيد..
This paper introduces a generalization of the concept of Set category
introduced in [10] by constructing the category - whose objects are
small ℒ - fuzzy sets in which the characteristic functions takes its values from
a complete distributive latt
ice, and its arrows are ℒ - fuzzy maps. After that
we construct a functor - between these two categories, in a
way that forgets the fuzziness of sets and maps, and formalizing the inclusion
functor - .
In addition, we study of the applications of universal arrows in category
- , and getting back to the classical state and comparing it with that
introduced in [10].
It's considered that، the ring of linear operator of vector
space and stilled as a source of many mathematicians in general and
algebreians particularly in introducing a new concepts in algebra
and ring theory. In this subject I. Kaplansky proved
the following
theorem: "The ring of linear operators of finite dimension vector
space is regular".
The object of this paper is studying of ring of linear operator
of vector space in abstract algebra point of view.
plot من أكثر توابع الرسم استخداماً في R وهو تابع عام Generic Function، أي أنه
يمتلك العديد من الطرائق حتى يلائم الكائنات الممررة له.
This paper shows that CIDEr-D, a traditional evaluation metric for image description, does not work properly on datasets where the number of words in the sentence is significantly greater than those in the MS COCO Captions dataset. We also show that
CIDEr-D has performance hampered by the lack of multiple reference sentences and high variance of sentence length. To bypass this problem, we introduce CIDEr-R, which improves CIDEr-D, making it more flexible in dealing with datasets with high sentence length variance. We demonstrate that CIDEr-R is more accurate and closer to human judgment than CIDEr-D; CIDEr-R is more robust regarding the number of available references. Our results reveal that using Self-Critical Sequence Training to optimize CIDEr-R generates descriptive captions. In contrast, when CIDEr-D is optimized, the generated captions' length tends to be similar to the reference length. However, the models also repeat several times the same word to increase the sentence length.
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