12 episodes were in the next step season 1.
12 episodes were in the next step season 1.
how many episodes are in the next step season 1?
12
köthe conjecture









































in mathematics, the köthe conjecture is a problem in ring theory, open . it is formulated in various ways. suppose that "r" is a ring. one way to state the conjecture is that if "r" has no nil ideal, other than {0}, then it has no nil one-sided ideal, other than {0}.









































this question was posed in 1930 by gottfried köthe (1905–1989). the köthe conjecture has been shown to be true for various classes of rings, such as polynomial identity rings and right noetherian rings, but a general solution remains elusive.









































section::::equivalent formulations.
köthe conjecture
bullet::::- riley (portrayed by brittany raymond) a shy contemporary and hip hop dancer who is emily's younger sister and matty's older sister and ella's ex-best friend. in season 1, she is a member of the e-girls but gets kicked out by her sister when she stands up to emily in favor of michelle. riley seems to have a crush on james in season1, then starts to date james in season 1.5, but later breaks up with him in season 2, after seeing him and his ex-girlfriend, beth kiss during their duet rehearsal. in season 2.5, riley makes a list of 20 tasks for james to complete before she would get back together with him. riley and james get back together and perform a duet at nationals. in season 3, she makes the internationals team, and befriends the mischievous english transfer ella, who starts to change riley and strain her relationship with james. ella is riley's best friend all the way up until internationals. at internationals, ella steals her solo in the female solo round and riley doesn't want to be friends with ella anymore. in the semifinals, they will have to face on england, ella's team, who already cheated the next step once already. ella's team, summerford dance academy, does a beautiful routine about a girl in the woods who is surrounded by scary trees. the next step do a routine where everyone does old-fashioned dancing and then james walks and the rest show him how to dance in that way. then james shows then hip-hop and the routine is a combination of two dances. the next step win the semifinals and ella asks riley if they can be friends again but riley refuses. in season 1, she has medium-length brown hair and brown eyes. in season 2, her hair is cut into a bob. in season 3, she grows her hair longer. she wears braces for the first 2 seasons, and gets them removed in season 3. in season 4, she becomes studio head when kate steps down in order to take a position as a judge in a dance competition in england. after the regionals loss, riley decides to leave the next step and go to business school.
list of the next step characters