It actually gets a little tricky if you use 'however' as a subordinate conjunction. If you join to independent clauses - as you did - then you must use the semi-colon with however. You must also put a comma in front of however, the way you would when however is used as a subordinate conjunction the beginning of the sentence.
He likes to go to market; however, he will not go this week.
Another important thing: however, when used as a Sub. Conj. can also go near the beginning of the sentence.
The man with the dog, however, could not dine at the restaurant.
Notice that 'the man with the dog' is not a dependent clause. Therefore ', however,' is correct and you do not need to use a semi-colon. Besides the placement of 'however,' this sentence is no different from:
However, the man with the dog could not dine at the restaurant.
Where a writer put the 'however' depends on the rhythm of the sentence. However, it is important to note that some grammar sticklers (influenced by Strunk and Whites Elements of Style), believe it is incorrect to start a sentence with 'however', when however is used as a subordinate conjunction.
The GMAT, however, does not subscribe to this "orthodoxy." I just thought I'd point this out because a google search on 'however' can yield conflicting info.
Hope that helps!
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