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If ab is algebraic over F and b 0, prove that a is

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 11SE Chapter 23

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 11SE

If ab is algebraic over F and b ? 0, prove that a is algebraic over F(b).

Step-by-Step Solution:
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▯ Personality Ch. 13 ▯ ESSAY ALERT: ▯ Four general Theoretical Approaches to Personality development 1. Psychoanalytic Approach: these theories assume that personality is shaped by several inner conflicting forces. 2. Trait/Genetic Approach: these theories assume that our personalities are made up of traits largely inherited form our biological parents and ancestors. 3. Humanistic Approach: these theories assume that we all strive for perfection and out of this striving personality develops. 4. Cognitive/social-learning approach: these theories assume that our personalities are shaped by the environment (i.e., that external forces shape personality)  Some believe that personality is learned  Note: No single approach is right or wrong. ▯ Psychoanalytic Approach  Freud’s Approach  Psychoanalytic Theory  Why has Freud’s theory been so impactful o It’s a GLOBAL theory  It attempts to explain all human behavior  Unfortunately, this is also the theory’s major drawback o It’s impossible to test or validate  Two instincts: sex and aggression o Were all trying to maximize ratifying the two instincts, while at the same time minimizing the possibility of being punished or feeling guilty.  Three levels of the mind (consciousness) o Conscious o Preconscious (tip of the tongue phenomenon) o Unconscious  Id  Ego  Superego  3 Components of Personality o Id: where the instinctual energy is located  Source of sexual/aggression energy  Pleasure principle  Needs immediate gratification  Demanding and irrational  No concern with morality/ethics/reality  If you didn’t have an Id you’d be beating people up and raping everyone o Ego: seeks sexual and aggressive pleasure, but only in accordance with reality.  Satisfies the id’s needs without causing the individual harm  Reality principle  Helps the id o Superego: moral faction of personality  Controls the id by internalizing parental authority  voice in the back of the head telling you to do the right thing  developed through upbringing  big weapon when ignored is guilt  Our unique personality depends, in part, on the relative strengths of our id, ego and superego  For example/// o When id strongest -> Ted Bundy (murder) o When superego strongest -> Mother Theresa (saints)  When three elements are out of balance “free-floating anxiety” develops.  The ego deals with getting rid of this anxiety through “ego defense mechanisms” o Behavioral strategies that we unconsciously use to distort or deny reality (read about these in the text) ▯ The development of personality  Freud focused primarily on the “life force” or sexual energy. He called this energy “libido” (or libidinal energy) o Force is in the id o Focuses on immediate sexual gratification o We are born with this pleasure-seeking energy o As we develop from infants…  This is libidinal energy focuses on different parts of our bodies at various ages  And, each body part brings actual sexual pleasure at that particular age. o So in the libidinal energy tries to attain pleasure at each stage  If pleasure is not attained at a certain stage, we get “stuck” at that stage  We become “fixated” at that state and this is produces abnormal behaviors later in life  Personality develops while passing through the stages o Freud’s Psychosexual Stages  1. Oral Stage (birth – 1.5 yrs): sexual energy centers on attaining pleasure form mouth region  2. Anal Stage (1.5-3yrs): pleasure is attained form the anal area. During potty training, children find bowel movements pleasurable.  Two basic adult personality types will develop if a child becomes fixated at the anal stage  Anal retentive (neat, clean, tidy)  Anal expulsive (messy, dirty, slobs) – didn’t get pleasure during anal stage  3. Phallic Stage (3-6 yrs): several landmark insights occur to the child during this stage:  the child learns the physiological difference between males and females  child becomes aware of sexuality  child becomes aware of the sexual nature of the relationship between mom and dad  Period of “homo-social bonding” – boys play with boys and girls play with girls – cooties  An important complex must be resolved at this stage for the child to grow into a sexually healthy adult  For males – Oedipus complex  For females – electra complex  Oedipal complex (males only) o A sexual desire for mother develops o A hatred for father develops o Fear of castration by father if he should learn of the love for the mother o Resolution: boys finally come to grips with the fact that they can’t have their mother sexually, and a warm relationship develops with mom and a “pal” relationship with dad o The boy beings to imitate dad’s behavior to get mom’s attention  Electra complex (females only) o The girl realizes she doesn’t have a penis o Develops “penis envy” (jealous of males for having penis) o Attaches love to father to “symbolically” attain a penis o A desire emerges to marry the father and have children with him o Resolution: most girls realize that marrying the father is impossible and begin to imitate the mother’s behavior in an effort to get the father’s attention  Note: when both complexes, resolution is attained by identifying with the same- gender parent in hopes of attaining the attention of opposite-gender parent.  4. Latency stage (6-12 yrs): here the libido takes a much needed break  5. Genital stage (13 & up): stage we are in now o Note:  Freud’s theory was based on the case-history of his own self-analysis and 12 mentally ill women!  Why was sex such an important facet of Freud’s theory  Freud believed that incorporating sex into his theory, it would give him a link to biology (a well- accepted science at the time). Trait Approach  Trait theories assume that our personalities consists of characteristics that are largely inherited from out parents and ancestors  Note: the goal of trait theories is to try to describe (not explain) personality  That is these theorists attempt with their research to identify the major dimensions on which everyone’s personality differs.  Big Give Personality Factors – OCEAN - o Emotional stability or neuroticism o Extraversion: reserved vs. outgoing o Openness: open to trying new things o Agreeableness: likely you are to agree or disagree o Conscientiousness: how aware you are your actions and their effects  For the Big Five characteristics, personality assessment questionnaires have been developed  Thus, we can calculate peoples’ personality scores on the 5 dimensions.  It is still under debate as to whether or not people’s traits are truly genetically determined or simply learned from environment  Recent data indicate that over 50% of individual differences in personality are, in fact, due to genetic influences o Study done at Minnesota called Minnesota Twin Studies

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Chapter 23, Problem 11SE is Solved
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Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

Since the solution to 11SE from 23 chapter was answered, more than 254 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Algebraic, prove. This expansive textbook survival guide covers 34 chapters, and 2038 solutions. Contemporary Abstract Algebra was written by and is associated to the ISBN: 9781133599708. This textbook survival guide was created for the textbook: Contemporary Abstract Algebra , edition: 8. The answer to “If ab is algebraic over F and b ? 0, prove that a is algebraic over F(b).” is broken down into a number of easy to follow steps, and 17 words. The full step-by-step solution to problem: 11SE from chapter: 23 was answered by , our top Math solution expert on 07/25/17, 05:55AM.

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If ab is algebraic over F and b 0, prove that a is