- ¥°. Ë»ëùÙÍøö
- Çö´ë´ë¼ö 1ÀÇ
¿¬¼ÓµÈ °ÀǷμ, ȯ(ring)°ú ü(field)ÀÇ ±âÃʰ³³ä¿¡ ´ëÇÏ¿©
°ÀÇÇÑ´Ù.
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À׿©È¯(factor ring), À̵¥¾Ë(ideals), Á¤¿ªÀÇ ºÐ¼öü, ¼ÒÀ̵¥¾Ë(prime
ideals), ±Ø´ëÀ̵¥¾Ë(maximal ideals), ±â¾à´ÙÇ×½Ä(irreducible
polynomials) µî°ú ü¿¡¼´Â È®´ëü(extension fields), ´ë¼öÀû
È®´ë(algebraic extensions), ±âÇÏÀÛµµ(construction), ºÐÇØÃ¼(splitting
fields), Àڱ⵿Çü±º(automorphism fields), ºÐ¸®È®´ëü(splitting
extension fields), À¯ÇÑü(finite fields), °¥·Î¾Æ Á¤¸®(Galois
theory), ºÒ°¡ÇØÀÎ ´ÙÇ×½Ä(Insolvability of the Quintic)¿¡
´ëÇÏ¿© °ÀÇÇÑ´Ù.
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- ¥². Îçî§ ¹× óÑÍÅÓñßö
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: J. B. Fraleigh
- A
first course in Abstract Algebra (6th edition)
- óÑÍÅÓñßö ±èÀÀÅÂ,
¹Ú½Â¾È îÊ, úÞÓÛÓÛâ¦ùÊ, ÀÌ¿ìÃâÆÇ»ç
- I.
N. Herstein, Topics in Algebra
-
- ¥³. Ë»ëùÛ°Ûö
- °¢ ´Ü¿øÀÇ ±âº»ÀûÀÎ
°³³äµéÀ» °ÀÇÇϰí, °¢ ´Ü¿øÀÇ ¿¬½À¹®Á¦´Â ÇлýµéÀÌ Ç®¾î¼
ÅäÀÇÇÏ¸ç ¿¬½À¹®Á¦ Ç®À̽ð£À» °®´Â´Ù.
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- ¥´. øÄʤ۰Ûö
- ñéÊàÍÅÞÛ
: 40 % õó
ଠ: 10 %
- Ñ¢ØÇÍÅÞÛ
: 40 % Ùýð¹Ç®ÀÌ
¹× ·¹Æ÷Æ® : 10 %
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- ¥µ. ñÎܬ Ë»ëùͪüñ
- Á¦ 1
ÁÖ Rings of polynomials over a field
- Á¦ 2
ÁÖ Factorization of polynomials over a field
- Á¦ 3
ÁÖ Homomorphisms and factor rings
- Á¦ 4
ÁÖ Prime and maximal ideals
- Á¦ 5
ÁÖ Introduction to extension fields
- Á¦ 6
ÁÖ Algebraic extensions
- Á¦ 7
ÁÖ Áß°£°í»ç
- Á¦ 8
ÁÖ Geometric constructions
- Á¦ 9
ÁÖ Finite fields
- Á¦ 10 ÁÖ
Automorphism of fields
- Á¦ 11 ÁÖ
The isomorphism extension theorem
- Á¦ 12 ÁÖ
Splitting fields
- Á¦ 13 ÁÖ
Separable extensions
- Á¦ 14 ÁÖ
Galois theory
- Á¦ 15 ÁÖ
±â¸»°í»ç
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