[Math] The first female algebraist in US/Britain

Question

Recently I dug up some biographical details of Lindsay Burch, of Hilbert-Burch Theorem fame, whose few papers have had quite an impact on commutative algebra. This made me curious about the first women who obtained PhDs in abstract algebra in the US and Britain.

Question 1: Who was the first woman to get a PhD in the US on a topic in algebra?

Potential answer: Mildred Sanderson, who obtained her PhD from Dickson in 1913 (published in Annals of Mathematics), and tragically died one year later. I found her name in Bell's "50 years of algebra in America, 1888-1938". Is that correct?

For Britain, I could not find any similar information. Burch got her PhD in 1967 under David Rees, but surely other women got British PhDs in algebra earlier. So:

Question 2: Who was the first woman to get a PhD in Great Britain on a topic in algebra?

Answer 1

I think a very honourable mention is the American Ida May Schottenfels, who did not receive a PhD, but who nevertheless was very active in mathematical research:

Ida May Schottenfels graduated from Northwestern University with a Bachelor of Arts degree in 1892. She then studied at Yale and the University of Chicago, earning a Masters degree in mathematics from Chicago in 1896. [...] In 1910 she was appointed head of the department of mathematics in Toledo University. In their study of "Women in the American Mathematical Research Community: 1891-1906" Fenster and Parshall cite Schottenfels as one of the two most "active" participants (along with Charlotte Angas Scott), listing her as giving 17 talks at mathematics conferences, publishing 3 papers, and attending 23 meetings and/or colloquia including those of the American Mathematical Society.

She was also the first mathematician to prove that there are two finite simple groups of the same order (namely of order $20160$). So although she did not receive a PhD, she surely seems to have deserved one!